Detection:

$Shortcuts2Remove = "VLC media player.lnk","Acrobat Reader.lnk"
$DesktopPath = "C:\Users\Public\Desktop" # Public and User Desktop: "C:\Users\*\Desktop\*", for Public Desktop shortcuts only: "C:\Users\Public\Desktop" 
$ShortcutsOnClient = Get-ChildItem $DesktopPath
$ShortcutsUnwanted = $ShortcutsOnClient | Where-Object -FilterScript {$_.Name -in $Shortcuts2Remove }

if (!$ShortcutsUnwanted) {
	Write-Host "All good, no shortcuts found. "
	exit 0
}else{
	Write-Host "Unwanted shortcut detected."
	Exit 1
}

Remediation:

$Shortcuts2Remove = "VLC media player.lnk", "Acrobat Reader.lnk"
$DesktopPath = "C:\Users\Public\Desktop" # Public and User Desktop: "C:\Users\*\Desktop\*", for Public Desktop shortcuts only: "C:\Users\Public\Desktop" 
$ShortcutsOnClient = Get-ChildItem $DesktopPath

try{
    $($ShortcutsOnClient | Where-Object -FilterScript {$_.Name -in $Shortcuts2Remove }) | Remove-Item -Force
    Write-Host "Unwanted shortcut(s) removed."
}catch{
    Write-Error "Error removing shortcut(s)"
}