Rashi (11b, DH v'Oso) writes that the Gemara is teaching a Chidush ("Rabusa"): even though the Tevalim originated from the great-great-grandfather who was a Yisrael, and therefore one might have thought that he must give the Terumah to the Kohen in the same way that the original owner (the great-great-grandfather) would have been obligated to do, nevertheless one is exempt from giving the Terumah. Rashi explains that the reason why one does not have to give the Terumah to a Kohen is that "Yad Kohen b'Emtza" -- "The hand of the Kohen is in the middle." This means that since the Tevalim passed through the intermediate hands of the Kohen grandfather, it is considered as though the Kohen grandfather had separated Terumah from the produce and bequeathed it to his Yisrael grandson. It follows that the Yisrael is not required to give the Terumah to a Kohen (but instead may sell it to a Kohen), because it is considered as though his grandfather Kohen already separated the Terumah for himself.

Rashi writes that the Din of the Gemara also would apply even if the Kohen grandfather had not inherited it from the Yisrael great-great-grandfather. The Yisrael grandson would be exempt from separating Terumah because the Kohen grandfather had already taken the Matanos for himself (as you wrote, that the Kohen is Chayav to be Mafrish but may keep the Matanos for himself).

Kol Tuv,

Dovid Bloom