A spokesperson said: "After a recent surge in goose numbers, we have decided to put them on a strict diet to discourage new arrivals. We are asking you to help out by not feeding the birds for the next few weeks. Thank you."
Despite having temporarily banned bird-feeding, trust sites sell bird food. The trust also has its own 31-product range of wild bird food.
A message on the Claremont Landscape Garden website had previously said: "Pick up a bag or two of bird seed from our kiosk and you will be guaranteed a warm welcome from our waterfowl when you enter the garden. All we ask for is a small donation."
The trust said: "The Canada goose is a non-native invasive species and as such they contribute to the pollution of water bodies, trample bank-side vegetation and damage farmers' grass crops. We advise our properties not to feed them because of the damage they can cause."