We leave ours to come back by itself. Having said that we only have one lot of weaners per year, and sometimes miss a year, so the ground has plenty of time to recover - we have permanent pens built underneath mature beech trees.
The ground comes back mainly as weeds but the next lot of pigs deal with those pretty swiftly, even the nettles.
My husband has been saying for years he is going to plant Jerusalem artichokes once the pigs are off, so that the next lot of pigs will reap the benefits, but he's not got round to it yet!