Try this code, I have modified the custom rendering parameter like the `Ajax Options` check box.

In this, the function takes as an input item you want to edit and field - either Final or Shared layout.

Also Write a log on every step:-

    $languages = @('en')
    
    $startPath = '/sitecore/content/xxx/xxx/Presentation/Partial Designs/Frenchs/Recipe'
    
    $renderingNames = @('Menu Wrapper')
    
    $renderingParamterToUpdate = "Ajax Call"
    
    $newRenderingParameterValue = "0"
    
    
    
    
    foreach($language in $languages){
    
        $items = Get-ChildItem -Path $startPath -Language $language -Recurse
    
        foreach($item in $items){
    
            Write-Host 'Updating Item: ' $item.Paths.FullPath
    
            foreach($itemRendering in Get-Rendering -Item $item -FinalLayout) {
    
                $renderingItem = Get-Item -Path master: -ID $itemRendering.ItemID    
    
                if($renderingNames -contains $renderingItem.Name){
    
                    Write-Host 'Found Rendering: ' $($renderingItem.Name)                
    
                    $parameters = Get-RenderingParameter -Rendering $itemRendering
    
                    if($parameters[$renderingParamterToUpdate] -ne $newRenderingParameterValue){
    
                        Write-Host 'Updating' $renderingParamterToUpdate -ForegroundColor Green
    
                        $parameters[$renderingParamterToUpdate] = $newRenderingParameterValue
    
                        $itemRendering | Set-RenderingParameter -Parameter $parameters |
    
                        Set-Rendering -Item $item -FinalLayout
    
                    }
    
                }
    
            }
    
        }
    
    }