Thomas Cook's sister airline, Condor, paid the money straight away and the aircraft avoided getting impounded.
"We first heard of the claim on Friday, when we were notified by the airport in Salzburg," Condor spokesman Johannes Winter told NBC News.
"Once we heard of it, we immediately paid. We are very sorry that it took this long."
Jonas Swarzenski, the legal chief of compensation company FlightRight, which represented the woman, said he believed it was an innocent blunder by the airline.
"Some airlines use the tactic of blocking requests or taking so long that people give up," he told NBC News.
"I think this was just an administrative mistake by the airline, the claim probably just got lost on somebody's desk."
Mr Swarzenski said only 15 per cent of travellers who were entitled to EU compensation ever actually made a claim.
According to the regulations, qualified passengers can claim financial compensation when they are denied from boarding, their flight is cancelled or their aircraft arrives more than three hours late, both within the EU and between EU and non-EU airports.
- news.com.au