Intune installed desktop shortcut needs to be removed

I created a desktop shortcut via intune windows app (win 32). Here is my script

New-Item -Path "c:" -Name "mem" -ItemType "directory" -Force

Copy-Item "S:\Shortcuts\UKG.ico" -Destination "c:\mem\UKG.ico"

$Shell = New-Object -ComObject ("WScript.Shell")

$ShortCut = $Shell.CreateShortcut("C:\users\public\desktop\UKG.lnk")

$ShortCut.TargetPath="-------------------------------------"

$Shortcut.Arguments="------------------------------------"

$ShortCut.IconLocation = "c:\mem\UKG.ico";

$ShortCut.Description = "UKG Shortcut";

$ShortCut.Save()

(I replaced the path with ————————)

The app works fine and copies the ico file from a network share and places it on the c drive in a folder it creates named mem. Now after creating the shortcut they have decided to use SSO which is a new address. I need to delete the ico file in the mem folder and remove the desktop shortcut. I created a simple script.

$ShortcutFile = "$env:Public\Desktop\UKG.lnk"

if (Test-Path $ShortcutFile){ Remove-Item $ShortcutFile }

else { Write-Output "Shortcut Not Found" }

To just delete the shortcut. When I run the script as an admin in powershell it works just fine. If I try and run the script in a normal powershell it fails and says it doesn't have access to the public desktop. I ran the file in Intune as just a script and it fails.  I converted it to an intunewin file and added it as an intune windows app (win 32). It successfuly runs on all my pcs but does not remove the icon. I'm at a loss and I really need to remove this icon so I can push the new one. Any suggestions on how to remove it via a script or app? I've checked into remediation scripts but that isn't going to be an option for now.