Thanks for the question and your trial of WebUI Test Studio. When recording and before converting to code, the 'Connect To pop-up window...' test step has a couple properties you can change for this.
You can change the PopUrl property to a partial Url without using the query string that will be constant for your application's popup. The IsUrlPartial property looks to already be set from the code you posted, and this property will help connect to the popup window without the query string.
You can also edit the code to do this as well, probably something like:
Please also edit the 'Close pop-up window...' test step similarly to the above as well.
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