Prefacing this with what a Query string is:
This Stack Overflow answer gives a few basic ways to get and use query parameters.
Looking at the Vue Docs it offers the Route Object, from which you can also get query parameters. There is another Stack Overflow answer that gives a demonstration of using it, along with an explanation in the comments.
UTM tags/codes are basically just another query paramter that get tacked on but dealt with elsewhere (often in an analytics platform, like Google Analytics). Here is an explanation of them, and here is specfic usage in Google Analytics.
If you don't need to use one, it can be safely ignored.
For some more basic information on how to deal with query strings in vanilla JavaScript, have a look at this page.
Retaining React UI state without localStorage or redux-persist