How to recover cost for damages after tenant damages

Rent Arrears

Tenant moved in in Apr20 after we did a full refurbishment (£13,000 spent on the property).
After 2 months arrears (£1,050), we served a section 21. She has finally left after we redirected her benefits.
We are spending £4,000 to put the property right: all the carpets needed replacing as she moved in a few pets without telling us and they absolutely stank, countless screws in most walls means we need to redecorate, professional clean and work on the garden that was never trimmed. To make matters worse, our previous letting agent messed up the guarantor's reference and it is not valid (see previous thread).
Our letting agent says it would be "unfair" to try charge the tenant for the full amount of refurbs?! The property was spotless when she moved in. We could go to small claim court but want to weigh the likelihood of winning vs the costs. Thanks.
John and Lila