Neighbor's Dog Jumping Into My Yard

Location: Maryland

Moved into a house around six months ago, I have a roughly waist high shared chain link fence with neighbors on either side. Around the time I moved in a family also moved in next door, but I believe they are renting. They have a large dog that appears to stay outside and have recently added a puppy, have had some issues in the past with the dog barking at odd hours and whenever my own dog or I are in the yard but have tried to be civil about it. Today their larger dog seemed to discover it could climb the shared fence, it has done so at least twice that I personally saw. So far there have been no altercations, both times when I saw it I brought by own dog inside and it eventually climbed back over. On the first occasion I went next door and knocked but no one answered, so I left a note explaining what had happened but I have not heard from them yet.

I'm mostly trying to figure out if animal control would be able to do much of anything about the dog climbing between fenced yards and if I need to worry about potential veterinary bills if anyone were harmed. My own dog at least did not appear to react aggressively to theirs, but I'm still wary because he has been seriously injured by another dog before. I also occasionally care for my mother's small dog that is a bit more reactive. I can't really afford to replace the fence with something taller at the moment and I doubt they would do so given they are only renting the property, so my only solution for the time being is to turn off the doggie door when I am not home and limit his time in the yard to when I am able to be outside supervising.

If they don't respond/take steps to further secure their dog, do I have any recourse other than calling animal control? Will animal control even do anything if the animal is not technically running loose?