GXM does not collect any data.
Some things might be read, like the URL or the state of downloads, or browsing activity, but all of that information is NEVER sent over the Internet. It's only used internally, by the extension, so the music can react to events.

If you enable "Mute while shopping", a list of shopping websites will be downloaded from jsDelivr.
However, you probably won't need to toggle it on unless you're using the Wii Shop Channel extension alongside GXM.
If you don't want to ping jsDelivr, don't flip that toggle! ^^;