[Ger-Poland-Volhynia] geography assistance: "Gruec"?

[Craig Schiller]

A bit of followup: after I posted my Gruec question this morning, a
relative of mine sent me some documents I didn't previously have, and
they change things considerably. My great-grandfather's Canadian
naturalization certificate does indeed list his birthplace as "Gruec",
but that would obviously have been typed up by a Canadian office clerk
-- so thanks to George for the "greetings" theory, because in light of
what I'm about to add, that suddenly feels extremely plausible after
all.

I was also provided with a copy of his confirmation certificate. It
has a birthplace on it. That birthplace does not say "Gruec" or
anything even close to it. I can't entirely make out exactly what it
does say (scanned copy of a photocopy of a photocopy of a 19th-century
document, you know the score), but what it does look like as far as I
can tell is "Borowitz something something" (the second something could
certainly be Kalisz, but I can't make heads or tails of the first
something.) And the document is annotated at the bottom as having been
filed in Rozhische, so wherever he was actually born they were clearly
living in the Lutsk area by the time my great-grandfather was a
teenager.

So instead of "Gruec", does the place name Borowitz (or something
similar to it) make sense to anyone in relation to Kalisz -- or in
relation to the Kalusz that's much closer to Lviv and Rozhische?

In the meantime, I'm going to sit here and wonder why nobody else ever
noticed this before.