Your mortgage application is underwritten based onthe information you provide. Once it has reached mortgage offer the underwriters will not revisit or rescore it unless they gain information that may have meant that a different lending decision could have been issued.
But the truth is that once your mortgage has been agreed then it is very unlikely that the lender will return back to your case unless it is presented with evidence that may change the lending decision. £4000 of credit card debt would certainly make a diffference on most cases but unless you make the lender aware of this it is extremely unlikely that they will revisit the case and the completion should happen