Until recently, when using GNU tar for creating base backups, you'd have
to ignore "file changed as we read it" and "file removed before we read
it" warnings, which would require a bit of craftiness if you wanted to
hide these messages while still seeing other warnings and errors from
tar.
As of GNU tar 1.23, there is a --warning option to selectively turn off
warnings. So you now could/should do something like this:
tar -C "$PGDATA" -c --warning=no-file-changed --warning=no-file-removed -f "$outname" .
This might be a good addition to the documentation, but I notice that we
don't have any recipe for calling tar in the documentation to begin
with.