They had boarded the Abu Dhabi-bound aircraft at Manchester Airport when they received a text message about their relative’s condition.
The flight, which had been taxiing towards the runway, returned to the gate so the couple could rush to their grandson’s bedside.
He died later on the same night.
The couple’s travel agent Becky Stephenson said the 30 March incident was “very unusual”.
“I’ve been in the travel business for 25 years and never heard of this happening,” she said.
Ms Stephenson, who is based in Bradford, praised the Etihad Airways pilot and said she had not heard of an airline going “above and beyond with their customer service” in such a way.
“I’m just really grateful that my customers could get back to see him,” she said: “My customers were so grateful that staff were very helpful and they were taken care of.”
“The flight still went ahead after the couple got off,” Ms Stephenson added.
“Etihad have said they can use the ticket again on a different date.
“But my customers are not thinking of when they’re flying back out again.”