You can always reduce the entrance if you suspect robbing. I would take the feeder off the entrance and put the jar (and the feeder if you like) over the inner cover hole. Either put the jar right on #8 hardware cloth right on the hole, or fill the remaining space with rags to keep the bees from filling it full of comb.
Entrance feeders are notorious for setting off robbing.
Entrance feeders are notorious for setting off robbing.