Is there a way to remove the 'Check Compatibility' link that appears under plugins in the plugin menu?
If so, how can I remove the link from a given set of plugins, and alternatively from all plugins at once?
That is part of WPML's functionality to check for known incompatibilities with 3rd party plugins. To my knowledge, there is no way to toggle that off.
As indicated elsewhere, this is actually part of the WMPL plugin.
To turn it off you can simply deactivate the additional installer plugin which is used to keep WMPL -and other 3rd party apps- up to date.