While not as fast as you would likely want, you can file a formal dispute of the collection with the CRA, which then requires forwarding to the debt collector, their investigation and response back to the CRA, with the CRA required to conclude their reinvestigation of the dispute within 30 days of its filing.
Legally, after the debt collector received notice of the correction to no debt due, they were required under FCRA 623(a)(2) to "promptly" update their reporting so as to maintain its current accuracy. Promptly would be in their next regular monthly reporting cycle, with deletion of the collection being the required reporting since there is no longer any delinquent debt upon which to conduct any collection.
Thus, legally, you should not have to file a dispute, as they are required to promptly initiate the required deletion.
Howver, a dispute will at least force an additionally statutory period for investigation and correction/deletion of their reporting.....
In the interim, have you showed the documentation establishng no debt in fact to your mortgage lendor? That may satisfy them regarding any underwriting requirement regarding removal of the collection.
However, that will not remove it from scoring, so until you get it deleted from your credit report, your score will still include the negative effect of the collection.
Perhaps a call to the original creditor and request that they contact the debt collector on your behalf........
