If any of the lower-level relays are attempting to gather the stale sites, then yes that stale request will be re-propagated back up the relay chain.
What occurs here is that the relay keeps a list of every site a client (or child relay) has requested, so it can track the version of the local copy of the site that it has cached. When a site is removed, clients unsubscribe and should no longer be requesting that site; but the relay still tries to query upstream to check for a new version of the stale site, at relay startup and possibly periodically after that.
Once a child relay asks for a new version of the site, the parent relay also adds the site back to the list of sites that it will check in the future.
Unless you have dozens or hundreds of these stale sites, it’s not really a problem but does add a lot of messages to the relay log which can make it more difficult to tell if there’s really a problem.
If you are letting subordinate sites deploy their own relays, you might share the cleanup procedure with them and ask them to go through it once a year or so. Then you can do the same on your higher-level relays every few months, eventually it’ll all get cleaned out.