Fact: In some counties it is illegal to deer hunt with the aid of dogs.
Hypothetical: A group of still hunters lease a property. A neighboring landowner has hunting dogs but had to give up hunting when the state made it illegal for him to do so on his own property. He used to lease all the neighboring property and is upset that others now have use of land that he considered to be his private hunting grounds. He loves to hear the dogs run a deer, so every weekend during season, he will let his dogs loose on his 20-acre farm just to hear them howl. When he does this, he does not possess any firearm or ammunition, so he is NOT hunting.
Of course his prized deer dogs jump deer and chase them all over the place. Not being able to read the NO TRESPASSING signs at the property boundary, the dogs cross over into the neighboring land leased by the club.
Now every person on that lease is subject to arrest for violating the law because of a dog chasing a deer.
How is that fair to the lease holders? They cannot stop the neighbor from turning his dogs loose every Friday, Saturday, and Sunday. Every time the landowner does this, the lease holders have zero recourse.
What should the club do?
There is no law holding an animal owner liable for their animal's trespass.