It sounds like you want to provide an app that will pay your subscribers to send SMS messages on your behalf. But since sending messages might cost the clients, you think your clients might cheat you by claiming to have sent the message without actually having sent it.
Unless there's a cryptographically trustworthy component baked inside the GSM modems that can provide a signed report of status back to you, there is likely no way to enforce it through cryptographic means. The clients are always able to provide their own implementations.
So instead, I would approach this with a random testing methodology. For each client, your server could randomly decide when to have them send a message to a trusted receiver. Maybe the test message is sent one time out of ten ordinary messages, or one message out of 50, something like that. Maybe you build the testing on a sliding scale. To start, one out of the first three or four is a test message, then as they continue to pass tests, you reduce the testing requirements. If someone is cheating, you won't receive the SMS, and you can investigate.
You have to be thoughtful in the design, of course. You can write it into the EULA agreement telling the clients that the system will periodically send test messages, and that they can be unsubscribed at your discretion. But you mustn't give them details of the testing methodology. If your clients can learn exactly which messages are test messages, they may still cheat and only respond to the tests. So your test messages must look like ordinary messages, and they must go to ordinary looking destinations. And if a message fails to arrive, you shouldn't immediately decide they've cheated you, as there are many other components that could have broken. You would have to investigate.
A different option would be to require that the clients provide proof of sending in the form of a copy of their billing statement. GSM systems record every SMS message destination. Perhaps you could arrange with the GSM providers to audit their records? Related, perhaps you could lease them the GSM modems and provide the accounts yourself, having the clients pay you for GSM service.