1. You need to ask the Letting Agent in writing for clarification on 'Vacating Sharer' as this in not in the Tenancy Agreement and which Legislation they are relying on for stating this. (its the legislation you need them to quote and give you a website link to it)
2. Is there a 'Break Clause' in the Tenancy Agreement and if so is the Tenant that wishes to leave wanting to leave before this 'Break Clause'? (if the tenant wishes to leave before that break clause they would be breaching the signed tenancy agreement and therefore need to negotiate with you the Landlord if they wish to leave before the date of that break clause)
3. Your question on the 'Right to Object' to the Letting Agent. You are the Landlord not them, you employed their services via a signed agreement and they must follow the directions of you the Landlord. (make sure and have a good read of what you signed when you employed the services of this letting agent). This is your property not theirs, they are only administering it etc on your behalf.
I just removed your name from post #4 above - anonymity is good, both here and on the net in general.
They can demand any amount they say you owe - that does NOT make it payable !!
Ignore but keep us posted.