Sadly, this issue is a known browser limitation. The glitch editor window can open a window for you, but without injecting some code into your project, there's no way the editor can know which page you're currently at.
The reasons for this make sense from a browser maker perspective: if you go to amazon.com, ideally amazon shouldn't know what you're doing on yahoo(!).
We'd love to solve this, hopefully browsers allow our use case for this in the future.
In the meantime, my recommendation is that you disable auto refreshing and manually reload from the page you want after making some changes.