The CRA's will only remove something if it is an error - you can appeal and stir up all the fuss you want but at the end of the day its either correct (and stays) or incorrect and has to be corrected.
Putting a statement re a CIFAS will have no impact what so ever. CIFAS is an automatic decline on all lending systems. There is a further fraud system which most lenders use called Hunter (
http://www.nhunter.co.uk ) - the lender could potentially have flagged you on that system as well.
Reading back through the post - the circumstances were that your pay slips said one thing and your mortgage provider did a job check they said you didn't earn that amount. This is fairly simple to remedy - your employer is required to provide a statement of the actual monies you earned together with any tax or national insurance paid. This should verify that your wage slips and the total earnings match and as such the CIFAS should be removed.
This isn't a question of whether CIFAS or the Lender feel like removing it under the Date Protection Act and the rules of reciprocity they are required to correct the information in a timely manner.