Private / Incognito embedded browser

Suggested change: Add an option on the mobile versions to run the custom chrome tab in private mode

So I use the custom Chrome tabs function and enjoy the ability to view links in Discord without opening a different app, but I recently discovered that when you use this feature, it (on Android at least) also pushes the links you visit to the history of your default browser. I would prefer if there was an option to have it be private.
From a user perspective it also doesn't make much sense that viewing something in Discord adds to your history in a different app. I understand the technology behind it enough to understand why this happens, but from a UX standpoint this seems like bad design (but I assume it's unintended behaviour).