Moth damage

Tenancy Deposits

Hello 12 months ago our tenant mentioned they had a moth problem in one room but they were treating it with a 'bomb' (they had lived there for 3 years prior to this so problem definitely arose during their tenancy). I asked them to let me know how the treatment went and then emailed details of a pest controller and suggested proper chemical treatment would be recommended and invited them to let me know if they wanted me to arrange. I never heard anything back. The tenant has just given notice and moved out. I went to look at vacant property and there is moth damage to every carpet in the house. They've hung little cardboard moth traps throughout the property and they are laden with dead moths, there are moths flying around. I've been advised to clean all curtains and replace all carpets. The tenant has agreed to clean the curtains and donate whatever he would have paid for end of tenancy carpet cleaning towards new carpets. However, having got a carpet quote he has nowhere near covered the cost of his neglect...can I deduct the remainder from his deposit?