Securing a shelf?

Does anyone have any ideas on how to secure this wicker shelf to the wall or something? It’s in my bathroom but my rude ass cats keep knocking it down & I’m tired of putting everything back. I know I can just shut the door to keep them out but it’s a very small bathroom & it gets extremely stuffy in there with the heat on 😅

Edit: Oh! Forgot to mention that it’s my landlords shelf that she furnished in the house! So little to no damage to it would be ideal.