Washer flooded my laundry room

I rent an apartment on the second floor (top floor for my unit). It has washer and dryer hookups and I brought my own. I have front load Samsung’s and have an issue with my socks getting stuck in the filter. It floods my laundry room every single time I have to open the trap (a few times a year) to get my sock out. I’m not aware it’s eaten a sock until it refuses to run the wash cycle completely.

My first question is, how can I stop this??

My second question is will it hurt the tile in my laundry room? It’s not linoleum but actual tile. I put as many towels down as I could to prevent the flooding but it was still too much. I cleaned as best as I could but can’t reach the center area under the washer, I even used BBQ tongs to try and push a towel to the area but it didn’t really work. The washer weighs too much for us to tip or pick up too and I don’t have a fan to put in front of it anymore.

Any other suggestions? I really need help. I don’t want to/can’t afford to pay for new flooring/tile when we move out. We take great care of our place otherwise, so this is rather stressful for me. Thank you for support and suggestions.

Edit: My SO called and said he isn’t sure it’s tile but rather a hard linoleum. It doesn’t have grouting either. It isn’t laid in 1 piece like all the linoleum I’ve seen.