Hi Dennis Bemer,
Get the source code form git and update the Jquery and rebuild it.
https://github.com/ObjectivityLtd/Mendix.RecaptchaWidget
Is it a dojo or react based widget? Since it uses jQuery I assume an older Dojo based widget. If so, the JS code also references the jQuery file in the lib folder. In that reference probably also the jQuery version is part of the name and reference. So, if that version is also loaded by another widget the widget will use that version again.
Be sure to update the widget references in the JavaScript code as well. They start with something like require(