You can only delete cost codes, categories, or vendors in Sage. You cannot delete them from hh2 or Procore.
Currently, there is no way for hh2 to recognize that a previously synced object was deleted from your Sage database. Therefore, even though you may delete a cost code, category, or vendor in Sage, the resources will continue to be displayed in Procore. This is a known limitation that will be fixed in a future release.