I don't feel right wearing leather/wool etc so would never keep anything if it was given as a present. I wouldn't feel right throwing it out either.
When I became vegan I gave all my leather items to friends and my woollens to Charity Bins.
A few years ago a friend, who is always thoughtful with buying me vegan presents, gave me perfume. She obviously didn't know about musk etc. I ended up selling it on eBay. I didn't feel bad coz if someone wants something, they will just buy it from somewhere else.
I received a gift from my mum, a leather jewellery box... I had been a vegetarian for about 4 or 5 years... and she knew perfectly well that I wouldn't like it. In fact, when she gave it to me she said, "you probably don't want it because its made of leather, right?" UGH!
I've never had this problem.
Whenever it gets gift time I call everyone and repeat "Please do not buy me cosmetics or after shave as they are probably tested on animals. PLEASE do not buy me leather/wool/silk/fur as I don't wear other animals skins".
Once you've told everyone it never happens. Especially when you reiterate it regularly.
BUT if it did happen to me I'd either:
A) Sell it and donate the money to an anti-industry (if it was wool I'd give it to an anti-mulesing/wool group for example).
B) I'd give it to a charity.