I have 2 icons from a previously removed program that persist
in my programs folder and shortcuts on start menu. Is there
any way to remove these?

Thanks

Very easily. With a file explorer got to Windows\Start Menu\Programs and simply delete the *.lnk files (the shortcut files) for the programs that you do not want to appear in the program screen.

To clear them from the Start Menu, delete them from the Start menu folder as well.

mAXIMum Addiction

  

Use file explorer and navigate to the Icons and then delete them, If it is in your programs folder navigate file explorer\my device\windows\ start menu\programs hold down stylis on Icon you want deleted and choose delete in popup
Edit @ Davrol you got fast typing skills

     

Thanks all