Tenant is threatening to file a case for deductions from security deposit

I have a registered agreement with my tenant which clearly mentions that tenant should pay for painting and cleaning charges, any damage done to furniture and sanity fitting while vacating. During vacating I had got quote from a reputed firm for painting and cleaning. Plus there are some damages done for which I deducted a nominal amount based on approximate cost of those repair. He had verbally agreed and I paid the balance security amount to him after removing painting/cleaning/repair charges. I also have email proof that he agreed to pay painting and cleaning charges. Now my tenant is harassing me to return him damage/repair charges and part of painting/cleaning as he feels that my estimates are inflated. He has no proof of the cost that he feels is justified. He is threatening to file a legal case against me to recover deducted security deposit. I have bills from a reputed firm to justify the actual cost that I have incurred for painting/cleaning/repair. What should I do?