Recycle the card however you wish. Those things are ephemeral and can't be used anyway after you check out and the hotel probably buys them in bulk.
And by "can't be used", I mean that your checkout date is encoded onto the card key and the room locks will reject any attempt to open the door past an expired checkout date in the same manner that you can't open someone else's door while you are at the hotel (or your own effin door half the time while you are still checked in).
That does not mean these keys can't be re-programmed with new room or checkout information. If you pay attention you will see the desk clerk shove the room key into a small box with a numeric key pad and hit a few keys et voilà you have a freshly programmed key ready to use (again). However if the key is physically damaged and won't take the reprogramming then the next stop is for it the rubbish bin. Here is a random link that claims to explain how these keys work Hotel Card Key Systems Explained
This of course raises the question of how easy it is to program a key in order to enter a room that is not yours. The funny thing is that while obvious, this question is actually moot as it is trivial to attack the lock itself with a simple electronic tool that exploits a fundamental design flaw in the how the locks themselves are programmed. Such a tool allows you to open all such locks with ease. I'll leave tracking down that exploit to the interested reader
Hotels are aware of this flaw, but it is going to be a long time before they roll out new door locks for every door that uses this style of pass key. Especially as a lot of hotels can't even seem to keep up with regular maintenance of normal in-room equipment.