Why would it matter if you had an AEG or not?
I mean it's not illegal to own a pellet gun. Really it's your personal business and the landlord must BY LAW
give you at least 24 hours notice before entering your premises, it doesn't matter what you signed in the contract if it was 6 hours or 12, BY LAW it is 24. (Some landlords will give you 48 hours notice in the contract, and they have to follow what it says in the contract but minimums have to be met in the landlord-tenant act).
Also they cannot enter your premises for non tenant-landlord issues. eg. they can enter if they suspect you have a grow-op, but cannot enter to gauge the kind of lifestyle you have.
Get a motion sensitive webcam or something and record if the landlord is entering your premises without your knowledge.
Logitech is quite nice, albeit a bit pricey (I love their products):