Good Morning and welcome! I am Dr. Loretta, a licensed veterinarian and I am happy to answer your question.
I am so sorry that it has taken so long to get to your question.
There are a few things that you can do about this visiting cat. he is doing this because of a territorial issue and this can respond to Feliway. This is a feline pheromone that acts as a calming agent and will decrease that cats anxiety so he will stop this behavior. This is available at the pet store. You can also place aluminum foil on the mat that will bother the cat so he will not use this mat. If this is not enough, then your vet will have medications that you can use on this cat if he is not feral. Ask your vet about this.
This LINK may explain in more detail.
Does that make sense to you?
Please let me know if you have ANY other questions. My goal is to give you 100% satisfaction and if you are not yet satisfied, please REPLY so I can clarify for you.Sincerely, ***** *****