As context, there is indeed a Gemara (Sanhedrin 76b) which prohibits returning a lost item to a gentile. The gemara seems to assume that it would be adding to the property that goyim stole from Jews. Rashi explains “One who returns a lost item to a gentile — he made a gentile equal to a Jew, and shows that he does not consider the returning of lost items a Divine commandment, for he does so even to a gentile, about whom he was not commanded.” Artscroll explains the prohibition to be following one's subjective sense of good and proper instead of Hashem's commandments.
The Rambam codifies this halacha (Hilchot gzela v'aveda 11:3) but adds it is permitted
if one returns to sanctify God's name, so that others will praise the
Jewish people and know that they are trustworthy, this is
praiseworthy.
In the case you describe
- since the check is not likely to be stolen money and
- since the Jew could make a kiddush Hashem out of it (by forwarding the check with a note signed in his name)
I see no reason not to return it in fulfillment of the mitzva of doing what is right and good in the eyes of Hashem (Dvarim 6:18).
And as fellow MY user Kazi bácsi pointed out (see here)
The Talmud Yerushalmi (Bava Metzi’ah 2:5) impresses upon us that
performing Kiddush Hashem is in fact imperative outweighing even the
Halakhah. Many of our greatest Sages went to extreme lengths in order
to sanctify God’s name before a gentile.
Rabbi Shimon Ben Shetach orders his students to return a jewel to a
gentile even though by Jewish Law they were entitled to keep it. Let
us add that the gentile was apparently an idol worshiper and a thief.
But no gentile is too lowly or corrupt for the power of Kiddush Hashem
to take effect. How important it was for Rabbi Shimon Ben Shetach to
hear a gentile exclaim the great words “Blessed is the Merciful the
God of the Jews”!
Of course, as for any other practical case which might happen to you, you should ask a rav.
