How can I stop syncing old text messages back to my phone?

[AC Question]

Every so often I get this pop up that asks if I want to sync my messages. I accidentally must have hit sync and now its putting old text messages back on my phone. Oh my gosh, it's using up battery and taking forever then I will have to go back and delete them all over again! How can I stop it from syncing during process?

 

[B. Diddy]

Welcome to Android Central! Which phone? Are you using the stock Messaging app, or a 3rd party one?