I would like to prevent the "Be careful! Your document may contain personal information that cannot be removed by the Document Inspector." dialog from being displayed when saving a document.

Found a programatic way to remove that confirmation. I hope this helps. In case if you found a better simple way, let me know :)

Clear-Host
$SourcePath = "D:\Worddoc.dotm"
$DestinationPath = "D:\Worddoc_removed.dotm"
if (-not (Test-Path $SourcePath)) {
    Write-Host "ERROR: File not found: $SourcePath" -ForegroundColor Red
    Read-Host "Press Enter to exit"
    exit
}
try {
    Write-Host "Opening Word application..." -ForegroundColor Yellow
    $Word = New-Object -ComObject Word.Application
    $Word.Visible = $false
    $Word.DisplayAlerts = 0
    # Retrieve PID of the newly created Word instance
    $wordProc = Get-Process -Name "WINWORD" | Sort-Object StartTime -Descending | Select-Object -First 1
    if (-not $wordProc) {
        Write-Host "ERROR: Could not locate WINWORD process." -ForegroundColor Red
        return
    }
    $wordPid = $wordProc.Id
    Write-Host "Word process started successfully (PID: $wordPid)" -ForegroundColor Green
    Write-Host "Starting UI Automation listener for dialogs..." -ForegroundColor Yellow
    $dismissJob = Start-Job -ScriptBlock {
        param($targetPid)
        Add-Type -AssemblyName UIAutomationClient
        Add-Type -AssemblyName UIAutomationTypes
        $procCondition = New-Object System.Windows.Automation.PropertyCondition(
            [System.Windows.Automation.AutomationElement]::ProcessIdProperty, 
            $targetPid
        )
        $maxAttempts = 40
        for ($i = 1; $i -le $maxAttempts; $i++) {
            $topLevelWindows = [System.Windows.Automation.AutomationElement]::RootElement.FindAll(
                [System.Windows.Automation.TreeScope]::Children, 
                $procCondition
            )
            $targetButton = $null
            foreach ($win in $topLevelWindows) {
                $targetButton = $win.FindFirst(
                    [System.Windows.Automation.TreeScope]::Descendants,
                    [System.Windows.Automation.AndCondition]::new(
                        [System.Windows.Automation.PropertyCondition]::new([System.Windows.Automation.AutomationElement]::AutomationIdProperty, "1"),
                        [System.Windows.Automation.PropertyCondition]::new([System.Windows.Automation.AutomationElement]::ClassNameProperty, "NetUIButton")
                    )
                )
                if ($targetButton) { break }
            }
            if ($targetButton) {
                Write-Output "UIA Handler: Found OK button in PID $targetPid"
                $invokePattern = $targetButton.GetCurrentPattern([System.Windows.Automation.InvokePattern]::Pattern)
                if ($invokePattern) {
                    $invokePattern.Invoke()
                    Write-Output "UIA Handler: Clicked OK button successfully."
                    return
                }
            }
            Start-Sleep -Milliseconds 500
        }
        Write-Output "UIA Handler: Timeout reached, no dialog detected."
    } -ArgumentList $wordPid
    Write-Host "Opening document: $SourcePath" -ForegroundColor Yellow
    $Doc = $Word.Documents.Open($SourcePath)
    $Doc.RemovePersonalInformation = $true
    Write-Host "Saving document..." -ForegroundColor Yellow
    $Doc.SaveAs([ref]$DestinationPath, [ref]15)
    Receive-Job -Job $dismissJob | ForEach-Object {
        Write-Host $_ -ForegroundColor Cyan
    }
    Write-Host "Save completed!" -ForegroundColor Green
    $Doc.Close([ref]$false)
    Write-Host "Document closed" -ForegroundColor Green
} catch {
    Write-Host "ERROR: $_" -ForegroundColor Red
} finally {
    if ($Word) {
        $Word.Quit()
        [System.Runtime.InteropServices.Marshal]::ReleaseComObject($Word) | Out-Null
        [System.GC]::Collect()
        [System.GC]::WaitForPendingFinalizers()
    }
    if ($dismissJob) {
        Stop-Job $dismissJob -ErrorAction SilentlyContinue
        Remove-Job $dismissJob -ErrorAction SilentlyContinue
    }
}
Write-Host "Done! File saved to: $DestinationPath" -ForegroundColor Green