Will a magnetized watch sustain damage during that time?

[Old Soul]

I am a college student taking physics and electrical engineering lab classes in which I will be working with and around magnets of about the strength of a fridge magnet. I don't want to leave my watch in the dorm but I also don't want it to become magnetized. If the watch is magnetized, could it damage any part of the movement from increased stress on the parts or anything? Thanks.