Or they are just a tad more arrogant and don't buy the British reinforcements as significant.
First of all, no Marines go to South Georgia.
Four AAR-capable large transports (borrowed C-141, etc.) flies from Ascension. Each Starlifter can carry 130 paratroopers. So, we drop 350 British paras plus palletized artillery or other kit to support the paras and RMs.
https://www.globalaircraft.org/planes/c-141_starlifter.pl
The garrison is now over 400 troops. Still a small force, possibly too small to deter the Argentinians - but if well equipped, likely sufficient to give the Argies a bad day.