Not a standard English word; possibly a technical or specialized term meaning to quote again or provide additional quotes.
Would combine be- prefix (thoroughly, about) + quote (Latin quotus 'how many' + -ation), but this formation is not attested in standard dictionaries.
This looks like it should exist—be-quote should mean 'to quote thoroughly' or 'to surround with quotes'—but English speakers never really needed it, so it never caught on in the language.
Complete word intelligence in one call. Free tier — 50 lookups/day.