There are any number of ways. First, the child support obligor is required to notify of the payment (many, however, don't). Second, the collection agency often monitors bank accounts, etc. Third, many settlements are part of lawsuits, meaning the settlement is on the court's record, so the agency can simply ask the computer to cross-reference people that owe against lawsuits to see if there is a match.
This answer is not to be considered a response to a specific legal issue in a specific jurisdiction - it is to be considered only a general response to a hypothetical scenario posed by the questioner. For specific legal advice, please consult with a licensed attorney in your jurisdiction.