I know this is an old question but in case someone else comes across this...
Paying off old debt can in some cases decrease your credit score.
In this particular case, before paying anything make sure they offer a Letter of Deletion otherwise known as a delete for payment. Be sure that they not only send the Letter of Deletion into the Credit Reporting Companies (which by the way are NOT government agencies) but to the original creditor so the debt isn't mistakenly resold to another debt collector then put on your credit report yet again.
Deleting the collection will improve your credit score. Also, keep in mind that your score isn't the ONLY thing mortgage companies, etc look at. They tend to go through the report so one less collection item is an improvement!
If you have anyone has questions about how this works, please don't hesitate to contact me. email@example.com
Hope this helps!