Of course, I don't use the Adobe Download Manager and even if you did use their download manager, you should be able to uninstall it normally from "Add/Remove Programs".. I would ignore the popup, or if possible, identify where the popup is coming from and stop it from occurring in the future..
Have you scanned the computer recently with a good malware removal tool such as Malwarebytes of SuperAntispyware?
Hope this helps.
I am being prompted via a popup to install a critical update from Adobe, the Adobe Software Removal Tool, strongly suggested by Adobe to remove Download Manager. Is this legit? I am running XP SP 2 on a Dell Dimension 3000 and have Adobe Reader installed.