I live in a condo, have been here a little over a year, I recieved a letter from my association about 4 months, stating that during one of their routine inspections, it was noted that I had several large snakes. and their hoa policy states no pets.
My snake room is locked (deadbolt) at all times, and I know for a fact that they had not been in my condo, I tossed the letter.
The difference with you is that you lease, they can & will make your life miserable, pay the $300. If you have concerns about snoopers, just buy a motion activated camera less than $100 on ebay (disguised as woking alarm clock) set it up in your bedroom to catch snoopers in the act, then go from there.