Aha. And how do you get your money then if the landlord says "I won't give it to you, you caused damage."? By doing nothing? This is bound to get interesting.
Not “doing nothing”, if the landlady does not hand over the deposit. But doing nothing that the landlady could still bring up as evidence in case of a legal dispute – because that threat looms if she withholds the deposit. However, the burden of proof lies solely with the landlady. Where did you read otherwise? I wonder why this didn’t come up during the handover. How do you even notice “declining adhesive strength”?
Report it to the liability insurance and let them decide/pay. I wouldn’t worry about it at all. If you damaged it, that’s exactly what it’s there for.
Excuse me? And then treat the landlady to a new floor at the expense of someone else’s insurance? She has her own insurance for that, namely the reserves from the rental income. And whether any damage exists at all is completely unclear.