As far as fixing it goes, you would be best off contacting a local alarm company that is willing to service a local (Non monitored) alarm system. Depending on the panel and brand and if the installers code is locked out or not it should be fairly easy. You could also fool the system into thinking there is a phone line by introducing 12VDC to it. Carefull though, if you don’t know anything about electonics you might just fry something. Check on top of the panel for the key.

If you send me a message with the model number I might be able to guide you through programming it out. Once again, depending on if the installers code has been changed or locked out.

Your service provider should be able to assist you with a "filter" that prevents the phone line from scrambling the alarm system.

We had to have one put in recently. Maybe that will help. If not, thanks for the 2 points.

Physically disconnecting the phone line from the security system won’t stop the alarm from freaking out. The system is probably set to alarm when it senses the absence of phone line current after a certain period of time. It shouldn’t alarm for a dropout of one second, so maybe your VoIP phone adaptor is acting up by not providing sufficient current for the security system to detect phone line presence.

Since you say the system is not being monitored, it would take an expert to deprogram the phone line monitor function from the system.