This is a sample script to show how to unpin a shortcut from the taskbar via Powershell without modules

unpinApp.ps1

# This is a sample script to show how to unpin a shortcut from the taskbar via Powershell without modules.

# The path of the shortcut .lnk file to be unpinned.
$Application = "$Home\AppData\Roaming\Microsoft\Internet Explorer\Quick Launch\User Pinned\TaskBar\App.lnk"

if (Test-Path -path "$Application"){
    (New-Object -ComObject shell.application).NameSpace($Application.Substring(0, $Application.LastIndexOf("\"))).ParseName($Application.Substring($Application.LastIndexOf("\") + 1)).Verbs() | Where-Object {
        $_.Name.replace('&', '') -match 'Unpin from taskbar'
    }
    | ForEach-Object {
        $_.DoIt()
    }
}
else {
    Write-Host "The shortcut $Application does not exist."
}