The best way to fix this is to open File Explorer and navigate to:
This folder is a "hidden" folder, however, you can simply copy and paste the path name above into the Windows Search box and press enter.
Look for the program(s) icons that you uninstalled and delete the remaining icons from this folder. Do not delete icons for programs that are still valid and installed.
Once you have removed the proper icons, you can then click the start menu again (it may take a second or five to refresh) now the uninstalled app icon should no longer show in the programs list.
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