delete the module from the INFO tab of the module and re-install it via the marketplace. All your data will still be there.
--edit--
Modules and skins are licensed for up to 2 domains, Intended so you can have developement version and a production version to test stuff out on, but you can have 2 production versions too.
If you have more than 2 domains you may have run into the problem where you are trying to run the same module on 3 domains. In this case you will see the "Purchase" option in the marketplace.
If you use Jamroom Hosting you can have as many domains as you like without extra charge.
Click the VIEW LICENSES button on the domains for your account here on jamroom.net to see which domains are using which modules and release some from domains you are not using:
https://www.jamroom.net/networklicense/licenses/profile_id=34/user_id=32
updated by @michael: 01/04/17 12:07:51PM