How can I get them to let me do it?
After renting out an apartment, the owner loses some of his rights regarding such a real estate object, namely, the owner cannot dispose of the apartment and use it.
The owner cannot come to the apartment at any time. The frequency of visits is specified in the contract. It is usually allowed to come every month. Moreover, the meeting must be arranged in advance. If there are no residents, it is forbidden to visit the apartment.
So, if the contract states that the owner has the right to visit the apartment, then you can demand it. If they don't let you in, call the police. After entering the home, document the damage. Damage to the home is grounds for terminating the lease agreement and later - recovery of damages in court.