If I remember correctly, the reason the father is mentioned here as being Greek was to explain why Timothy wasn’t circumcised.
Why circumcise one, but not the other?:
1 And he came also to Derbe and to Lystra: and behold, a certain disciple was there, named
Timothy, the son of a Jewess that believed; but his father was a Greek.
2 The same was well reported of by the brethren that were at Lystra and Iconium.
3 Him would Paul have to go forth with him; and
he took and circumcised him because of the Jews that were in those parts: for they all knew that his father was a Greek. Acts 16
3 But
not even Titus who was with me, being a Greek,
was compelled to be circumcised:
4 and that because of
the false brethren privily brought in, who came in privily to spy out our liberty which we have in Christ Jesus, that they might bring us into bondage:
5 to whom we gave place in the way of subjection, no, not for an hour; that the truth of the gospel might continue with you. Gal 2