I've never caught a Bird Hunters dog in a trap but I have caught one in a snare.
I told the guy about where the snares were set (for Coyotes) and he went to that area. Told me he "lost" his dog in the weeds & had to look for him. There the dog was, sitting in the middle of the trail I'd set. NO PROBLEM he simply released the dog. He though it was kinda funny the way the dog just sat down and waited for him to come after him.
Some people get a bit "ruffled" about Trappers but for others It's No Problem..... Just something we have to live/cope with I guess......
If I were you grovetrapper, I'd contact the guy with the dog and tell him about your traps in that area. He can't say he wasn't informed, before hand anyway. You have just as much right to the property as he does.
That right there is the best answer.
A responsibile hunter would ask the land owner if there were traps on the property.
Then they have a choice of hunting or not.
As stated you have just as much right as the hunter.
You both have choices.
Only difference is the land owner wants you there for animal controll as a benefit to there crops or livestock.
The bird hunter is there for his own pleasure(
NOTHING WRONG WITH THAT)and should respect your responsibility to the landowner.