What should I do with an old thermostat?
If your security system is monitored for a monthly fee I would save it. There is the possibility that it won't function if the service is terminated. If a year from now you decide you no longer want the service you may be in need of a new thermostat. Although it appears to be relatively new verify it doesn't contain mercury, even if it doesn't try to recycle it when you do throw it out.