Here's my Delete Sync AppleScript. It's mostly the same as the Backup Folder AppleScript but the processing loop is changed.

set m_source_folder to ""
set m_destination_folder to ""
set m_deleted_folder to true

tell application "Finder"
  
  -- Get destination and source folders
  if (m_destination_folder = "") then
    set m_destination_folder to choose folder with prompt "Delete items from this folder:"
  end if
  if (m_source_folder = "") then
    set m_source_folder to choose folder with prompt "Use this folder to check against:"
  end if
  if (m_deleted_folder is true) then
    set m_deleted_folder to choose folder with prompt "Deleted items will be moved to this folder:"
  end if
  
  -- Log start time
  set l_start_time to current date
  log "+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++"
  log "Delete destination: " & m_destination_folder as string
  log "Delete source: " & m_source_folder as string
  log "Deleted folder: " & m_deleted_folder as string
  log "Delete start time: " & l_start_time as string
  log "+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++"
  
  -- Get destination folder length so that we can strip it out of each destination folder's path
  set l_destination_length to (length of (m_destination_folder as string)) + 1
  
  -- Convert folder class to string (":...")
  set l_source_folder_string to m_source_folder as string
  
  -- Set queue items and start main repeat loop.
  set l_pending_folders to {m_destination_folder}
  
  -- While items remain in queue, process each one
  repeat while ((length of l_pending_folders) > 0)
    
    -- Remove the first item from l_pending_folders
    set l_current_folder to first item of l_pending_folders
    if (length of l_pending_folders = 1) then
      set l_pending_folders to {}
    else
      set l_pending_folders to rest of l_pending_folders
    end if
    
    -- Log current folder
    log "Checking folder " & l_current_folder as string
    
    -- Determine source folder string
    set l_string to l_current_folder as string
    try
      set l_string to (text l_destination_length through (length of l_string) of l_string)
    on error l_error
      -- error if this is the destination folder base string
      set l_string to ""
    end try
    set l_string to l_source_folder_string & l_string
    
    -- Determine source folder.
    -- Note that source folder must exist.
    set l_source_folder to alias l_string
    
    -- Cycle through items in the current folder and process each item
    set l_items to items of l_current_folder
    
    repeat with l_destination_item in l_items
      
      set l_delete_item to false
      set l_source_item to ""
      
      -- See if the item exists at the destination
      try
        set l_source_item to get item (name of l_destination_item) of l_source_folder
      on error l_error
        set l_delete_item to true
      end try
      
      -- If we need to delete the item...
      if (l_delete_item is true) then
        
        -- Log event
        log "----Deleting item " & l_destination_item as string
        
        -- Delete source 
        try
          if (class of m_deleted_folder is alias) then
            move l_destination_item to m_deleted_folder with replacing
          else
            delete l_destination_item
          end if
        on error l_error
          log "****" & l_error
        end try
        
      end if
      
      -- If source item is a folder and wasn't deleted, add it to pending folders list
      if (l_delete_item is false and class of l_destination_item is folder) then
        set l_pending_folders to l_pending_folders & {l_destination_item}
      end if
    end repeat
    
  end repeat
  
  -- Log end time
  log "============================================================="
  log "Delete destination: " & m_destination_folder as string
  log "Delete source: " & m_source_folder as string
  log "Deleted folder: " & m_deleted_folder as string
  log "Delete start time: " & l_start_time as string
  log "Delete end time: " & (current date)
  log "============================================================="
end tell