Our garden has always had squirrels 2-4 at a time and we put up with the small amt of damage they did until one got into our loft space and chewed up a ton of insulating fibre and the modem cable.
We were advised by the council to use a trap which we purchased from an agricultural supplier. I seem to remember it was quite expensive to buy but it was 8 years ago and I'm not sure.
We caught the squirrel very easily and then drove to a large wood about 10 miles away and set it free.( be very careful if you do this they become savage in the cage, wear thick gloves to carry the cage.)
The other squirrels in the garden seemed to disappear for a few years. Perhaps we caught the only male, or only female and the others left in search of mates.
They are now back with us but we are putting up with them for now. The cage is still there!