Does deleting stages in Administration also delete from the managed package's picklist?

I have a customer who only uses two stages and therefore deleted the out-of-the-box stages that came in their Gainsight instance (new customer, kickoff, launched, churned) from the Administration home page section. 

This works as expected when filtering by stage against SFDC objects - i.e. when I source the opportunity in a report and add a stage filter, I only see the two stages that are available in the Administration tab. 

However, Gainsight Connect still shows the out-of-the-box stages in addition to the two stages that my customer wants. So it's a little confusing, for example, when they are putting together a scorecard report and see 6 available customer stages rather than the 2 they use. 

So my question is - does deleting a stage from Gainsight's Administration not delete that stage from the picklist in the managed package backend? I'm assuming Gainsight Connect is just pulling from the managed package picklist in SFDC, hence why we're seeing those extra picklist values. Can someone confirm? Thanks!