The association between SIM card and phone number is in your carrier's systems, not your phone, so you cannot change that.
So what is the app actually checking: your phone number or your IMSI (SIM number)? Have you changed the SIM or phone number since you last used the app? If so, did the app developer seriously not make provision for that happening (because people do change these things)? And, as asked above, which app is this?