Gary - MapSearch is simply a tool used to identify title information. It is not definitive re the registered extents for example and any mismatch would not be a barrier to completing an application to update the register itself.
If someone wishes to query the MapSearch extent and highlight a mismatch then they can do so by contacting us
Public guidance: dealing with land and property - GOV.UK
We do not charge a fee. The fee your conveyancer is quoting is their own professional fee for doing the work so to speak.