I'm answering this without spoiler tags, if that's alright. If you haven't seen Season 3 so far, you've been warned.
First, I wouldn't assume that Locke(I think that's who does the deed) would know about where Bolton's loyalties lie. The more people who know, the more someone might let it slip and out Bolton to someone more loyal to Robb. I certainly wouldn't trust that information unless absolutely necessary.
Second, I think that if Tywin presses the issue Bolton can pass the blame on Locke and offer him up to Tywin. In the show, it's not been shown how Tywin will react yet. We'll see what Season 4 brings.
In the books however, it's a completely different matter. The issue is addressed more directly, and it interesting enough to post.
A sellsword company led by Vargo Hoat under the pay of Roose Bolton turned from the Lannister's side to Robb's. After the Lannister's victory at the Battle of the Blackwater, Vargo was worried about Roose Bolton shifting allegiances back to the Lannisters. They captured Jaime and Brienne and in order to prevent Bolton turning sides again, he amputates Jaime's hand so the Lannisters place blame on Bolton(and make Tywin angry, as you suspected would happen).
In the books, Bolton releases Jaime if he absolves Bolton of any blame for the loss of his hand. Jaime agrees and he departs for King's Landing similarly as in the show.
The Books have a more satisfying reasoning behind it all, personally. The TV series doesn't go into much detail, but you expect to have some things left hanging with so much going on. They handled it fairly well as far as I'm concerned.