Hilchos Bikkurim 9:19

The gifts given to a kohein may not be skinned, nor may one pour boiling water on the hide in order to remove the hair. Rather, it is given to the kohein along with the skin and the wool. We give the abomasum to a kohein with the fat that is on it. The custom has become for the kohanim to give the fat of the abomasum to the owners.

Hilchos Bikkurim 9:20

Women from kohein families are allowed to eat the gifts even if they’re married to Yisroel men; this is because the gifts aren’t sanctified. Not only that, the woman’s husband may “ride on her coattails” and eat them as well. A chalalah,* however, may not eat the gifts. This is because a chalal** doesn’t count as a kohein. If a kohein wants to sell or give away the gifts, he may do so, not only to Jews, but also to non-Jews or even to feed to dogs. This is because the gifts are not sanctified in any way.

*A woman born from a relationship that is prohibited to kohanim, or a woman prohibited to kohanim and who engages in intimacy with a kohein.

**The son of a kohein with a prohibited relation.