@Windows 10 User, since you say IE wasn't removed, which is not what I see, do you maybe integrate a cumulative update or something
after removals in a second session before installing it?
If I see IE leftovers it would get fixed, there is nothing you would need to run after install. But since you got different results yourself there must be something else at play.
NTLite always rebuilds an image when saving it. You can initiate manually on the Source page, right-click on a WIM and choose Convert - Rebuild. Image must be unloaded/unmounted first of course.
Let me know if the icon or IE leftover is the issue so I can test for, it cannot be randomly one or the other, please see what else you might be doing so I can repeat the process.
Thanks.