There are about 2,000 golden eagles in Scotland at any given time. They eat about 500g of meat each per day year-round. Mixture of carrion, hares, grouse, crows, rats, rabbits and anything else they can get their claws into. Say 500kg of grouse a day, 180 tonnes a year?
The density of grouse on an industrial moor is about 1.5 per hectare so the Scottish population on the 1.6 million hectares of moor is 2.3 million birds, total mass 1,600 tonnes.
So the loss is non-trivial but you wonder why they risk six months in prison over it.
The answer is the demanding nature of the rich people who pay to shoot the birds. They think of themselves as very special and are incandescent if large numbers of grouse are not put in front of them. Grouse are very scared of eagles and will bug out or sit cowering if they see one. This makes the actual shoot hard to manage and is the reason the estates kill birds of prey.
What needs regulated, as ever, is rich people's greed and sense of entitlement.