The "Greeks" with whom the Turks mixed were not Greeks from mainland Greece. Greeks in Anatolia had the CHG as well as the Neolithic Anatolian heritage.
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Code:Anatolian:TUR_Arslantepe_EBA,0.1032945,0.1546142,-0.0594908,-0.089552,-0.0198495,-0.0290045,0.0017625,-0.010615,-0.0177422,0.012483,0.0054808,0.0017985,-0.005649,0.003888,-0.0106202,-0.0020882,0.0073667,0.0017735,0.0029852,0.0010945,-0.001435,0.004235,-0.0016332,-0.0043682,-0.000509
Turkic:West_Turkic:KAZ_Kipchak:DA179,0.067156,-0.041637,-0.012822,-0.005814,-0.018773,0.002789,0.001645,0.009,-0.0045,-0.011481,-0.01088,3e-04,0.004311,0.000963,0.000271,0.016706,0.012256,-0.007601,0.006159,0.000625,-0.000749,0.002844,0.001849,0.01458,-0.006706
Turkic:Gokturk:DA89_noUDG.SG,0.079676,-0.074134,0.015085,0.020672,-0.05201,0.002231,0.005405,0.004846,-0.025156,-0.013121,-0.016564,-0.001049,-0.001635,-0.009909,0,0.007955,-0.005346,0.0019,0.008547,0.000625,-0.007237,0.001731,-0.014173,-0.008555,0.003592
Turkic:Ottoman_1400ad:MA2195,0.072847,-0.144205,0.035449,-0.000969,-0.045855,-0.02008,0.009165,0.004154,-0.014112,-0.011299,-0.006008,-0.006594,-0.001189,-0.013349,0.004072,0.00053,0.005476,0.002914,-0.005405,0.007879,-0.012104,0.000495,-0.011339,-0.006386,-0.004191
Turkic:KAZ_Karakhanid:DA204,0.068294,-0.155376,0.032055,0.014535,-0.05601,0,0.002585,0.003692,-0.010226,-0.015126,-0.018675,-0.002847,0.001189,-0.016928,0.009365,0.00358,-0.01695,0.000887,0.005028,0.001751,-0.018343,0.003215,-0.00456,-0.006627,-0.007185
Turkic:KAZ_Karakhanid:DA205,0.05805,-0.199044,0.027907,0.002907,-0.041854,-0.01004,0.00705,0.005307,-0.011862,-0.007472,-0.010555,-0.001199,-0.000446,-0.007156,0.012758,0.007955,0.002086,0.001774,0.000377,0.006003,-0.015348,0.003833,-0.00419,-0.003735,-0.002515
Turkic:KAZ_Karluk:DA222,0.064879,-0.158423,0.023004,0.000969,-0.05601,-0.00753,0.00658,0.014999,-0.01493,-0.010934,-0.018188,0.001649,0,-0.004266,0.0076,-0.000928,-0.006519,0.005448,0.01081,0.001501,-0.015473,-0.003586,-0.003328,-0.004579,0.005987
Turkic:KAZ_Karluk:DA230,0.061464,-0.145221,0.011691,-0.002584,-0.037545,0.001673,0.00329,0.009461,-0.01718,-0.009476,-0.021922,-0.003297,0,-0.001101,0.013979,-0.006895,-0.020992,0.002914,0.003771,-0.005378,-0.004492,-0.000742,0.00037,0.000602,0.002155
Turkic:KAZ_Kimak:DA87,0.080814,-0.140143,0.043746,0.027455,-0.050471,-0.011435,0.00376,0.000462,-0.020043,-0.018224,-0.007632,-0.003147,-0.006244,-0.002064,0.008822,0.007425,-0.019558,0.005448,-0.003142,-0.027013,-0.02533,-0.010387,-0.001479,-0.010363,0.001317
Turkic:DA228_noUDG.SG,0.081953,-0.098506,0.034695,0.006783,0.000923,0.003626,0.00564,0.011999,-0.010635,-0.006196,-0.024845,-0.008243,-0.004757,-0.004129,0.001629,0.002784,0.002217,-0.001014,-0.001508,0.001501,-0.005366,0.013478,-0.000123,0.006025,0.002874
Turkic:DA142_noUDG.SG,0.087644,-0.092413,0.05242,0.0323,-0.037545,-0.006136,0.00376,0.006923,-0.007158,-0.017495,-0.007957,-0.00045,0.003568,-0.006055,-0.004207,-0.006629,-0.008736,0.0019,0.002011,-0.003126,-0.004492,0.009769,0.004807,-0.00012,-0.00467
Turkic:DA94_noUDG.SG,0.081953,-0.139128,0.05242,0.039729,-0.058165,-0.010877,0.01034,0.014769,-0.005931,-0.006925,-0.01088,-0.014837,0.004014,-0.023396,0.006515,0.012463,-0.002086,-0.001014,0.004777,0.001376,-0.018842,0.000618,-0.015776,0.011568,0.001796
Turkic:DA23_noUDG.SG,0.073985,-0.209199,0.064488,0.015181,-0.057241,-0.014502,0.00987,0.017307,-0.003886,-0.001276,-0.017538,-0.00015,0.002081,-0.01156,0.002443,0.004906,-0.000391,0.002027,0.004399,0.007379,-0.01984,-0.000742,-0.007395,-0.010965,0.002994
Turkic:DA124_noUDG.SG,0.07057,-0.182795,0.02753,-0.005168,-0.042162,-0.006414,0.00893,0.004615,-0.015135,0.001093,-0.006171,0.005995,-0.003865,-0.002202,-0.001493,0.001061,-0.01004,-0.001647,0.00088,-0.004252,-0.02533,0.004575,-0.008504,-0.000723,-0.011735
Turkic:DA126_noUDG.SG,0.071709,-0.140143,0.03017,0.010336,-0.028313,0.013945,0.018801,0.005077,-0.018407,-0.019681,-0.018512,-0.00045,-0.006095,-0.026148,0.011265,0.001458,0.00326,-0.00114,0.004022,-0.001251,-0.011355,0.003833,0.001479,0.004579,-0.008263
Turkic:CHK004,0.060326,-0.118817,0.011691,0.001615,-0.044008,-0.000558,0.012221,0.006692,-0.019839,-0.016037,-0.013803,-0.002548,0.005352,-0.017891,0.016151,0.012198,-0.003912,0.000633,-0.005656,-0.002751,-0.006738,-0.007914,0.00456,-0.00241,0.000718
Turkic:DA93_noUDG.SG,0.069432,-0.183811,0.069767,0.030685,-0.055395,-0.007809,0.00047,0.001615,-0.011658,-0.020228,-0.011692,-0.001649,0.001635,-0.019542,0.009093,0.001989,-0.005476,-0.003547,-0.002011,0.004127,-0.023583,0.009521,-0.002342,-0.000843,0.000838
Anatolian:TUR_Kaman-Kalehoyuk_MLBA,0.1050018,0.1515678,-0.042332,-0.082365,-0.0040775,-0.0274705,-0.0024088,-0.0077882,-0.011402,0.028429,0.0097435,0.007006,-0.0120788,0.0030965,-0.0138435,-0.004475,0.0116693,-0.0021538,0.0087988,-0.00741,-0.0031817,0.0061828,-0.0048065,0.0030725,-0.001407
Anatolian:TUR_Ovaoren_EBA,0.0990263,0.151991,-0.0452547,-0.0812883,-0.0043087,-0.022776,-0.0019583,-0.0081533,-0.0088627,0.027457,0.0073077,0.0044463,-0.0130327,-0.0065143,-0.0147933,-0.000442,0.0126037,0.003801,0.0043577,-0.0017507,0.0003327,0.0055233,-0.0028757,0.0011247,-0.0024747
Anatolian:TUR_Isparta_EBA,0.114582,0.1590993,-0.040226,-0.0802117,-0.004411,-0.024728,7.83e-05,-0.003846,-0.0115897,0.0329847,0.0068207,0.003497,-0.012686,-0.003257,-0.0225297,0.0032263,0.0214267,-0.0024493,0.0070393,-0.0007087,-0.0044507,-0.003215,0.000575,-0.003213,-0.0022353
Iranic:I2327,0.09675,0.111708,-0.073916,-0.035207,-0.048624,0.00502,-0.00141,-0.000231,-0.041314,-0.018224,0.003735,3e-04,0.009514,-0.00289,0.001357,0.011138,-0.008214,0.010388,0.004651,-0.003502,-0.001747,-0.012365,-0.002588,-0.008194,0.006706
Caucasus:I1633,0.104717,0.125926,-0.069767,-0.039729,-0.044316,0.003068,0.016451,-0.01223,-0.062789,-0.025513,0.004547,0.005845,-0.016353,0.001789,0.011265,-0.000265,0.009257,-0.001647,0.003268,-0.003252,0.007736,-0.004822,0.003328,-0.003615,-0.003233
Turkish Turks are not a monolith, it's a very diverse group of people stemming from Anatolian, Iranic, Caucasus, Turkic (ofc) and other groups in the region. Percentages vary per region. You can't say all Turks have Greek blood. Many do, but not all. Some are more Caucasus leaning, others have elevated Turkic in their genome and some are assimilated Kurds. Some are all at once. I don't see why that is a bad thing (aside from assimilation if it was forceful, of course). But yes, there are Turkish Turks that have Greek heritage or something else thats similar to modern day Greeks. There's also an overlap with ancient Anatolians and Greeks.
This is also why Turkish Turks have a broad range of phenotypes, as they aren't descended from one ethnic group (barely anyone is, most Northwest Asians are geneticaally very heterogenous). There are quite a lot of Southeast European-passing Turkish Turks, which could signify at least partial Greek or Balkan genetics in those individuals but not the entire population because, once again, Turkish Turks aren't a monolith.
This phenomenon is, as aforementioned, not just present in Turkish Turks but other groups in the region as well such as Kurds, Laz, other Turkic groups like Yörük Turks and Caucasus peoples. Turkish Turks are seen as Turkic, Kurds are seen as Iranic, Armenians are seen as Kavkaz and these groups will boast about their Iranic/Turkic/Kavkaz pure blood but when you make them take a DNA test you'll see how close they plot together as compared to other groups. Why? Because they all have each others DNA.
Long story short there's no way you can generalize Turkish Turks regarding Greek blood or any other non-Turkic blood because Turkish Turks are very diverse just like their neighbours. Also, there's no shame in a Turkish Turk having Greek, Kurdish or Armenian blood, and of course the same way around AS LONG AS it wasn't forceful.