Just when it seemed the fuss was starting to die down following this week's spectacular fallout between two of the world's best-known golfers, O'Grady entered the debate by giving an interview to Sky Sports television.
"I deeply regret using an inappropriate word in a live interview...for which I unreservedly apologise," O'Grady said in a statement at the PGA Championship.
Earlier in the day, the tour chief said: "We know the connotation in the United States.
"All races play on the European Tour and that's how we want to keep it. Most of Sergio's friends are coloured athletes in the United States and he is absolutely abject in his apology and we accepted it."
Garcia said sorry 11 times on Wednesday and used the word apology on five occasions after causing a furore by making a "fried chicken" jibe at world number one Woods.
The Spaniard said his comment, made at the European Tour Player of the Year awards dinner on Tuesday, was "stupid and out of place" and said he regretted it the moment he uttered it.
Fourteen-times major winner Woods, whose relationship with the Spaniard has always been frosty, was in unforgiving mood when he gave his reaction to Garcia's jibe.
"The comment that was made wasn't silly. It was wrong, hurtful and clearly inappropriate," the American said on his Twitter account.
Garcia's remark came when he was asked on stage whether he would be inviting Woods for dinner during next month's U.S. Open in Pennsylvania.
"We will have him round every night," said the world number 14. "We will serve fried chicken."
Fried chicken has become a racial stereotype in the US when referring to African-Americans, a reference to the days before the abolition of slavery when chicken was believed to be a staple part of the diet.
O'Grady and US PGA Tour chief executive Tim Finchem were present at the awards dinner and both declined to punish European Ryder Cup stalwart Garcia for his remark.
"It's very unfortunate and we are in the middle of it," O'Grady told Sky on Thursday. "We spoke to Sergio and, after what was really a very full and frank discussion on the whole issue, decided to accept his really heartfelt apology.
"We were convinced he was trying to be funny - that it was a light-hearted remark. There is no need for any further disciplinary action because it has gone so deep with him and all our players think the same way.
"We are aware of his arguments and his discussion with Tiger Woods which really quite frankly has no real place either, he accepts that," said O'Grady.
"Tiger himself has...said it's time to get on and play golf and we want to get on with our flagship event which is set up so well this week."
O'Grady said this sort of incident had no place on the European Tour.
"There's absolutely no cosiness about this at all. We take it very seriously as does he (Garcia)," added O'Grady.
"He has convinced us just how seriously he takes it and that's why we've had to draw a line under this thing."
Garcia and Woods fell out earlier this month after an incident at the Players Championship in Florida.
The Spaniard blamed a roar from the crowd watching Woods for an errant shot when the two men were playing in the same group.
The gallery erupted during Garcia's backswing upon seeing the world number one reach for his five-wood for a daring escape from a tee shot that finished deep into the trees.
The pair subsequently made clear they have never been the best of friends but Garcia said that he had already tried to contact Woods in a bid to make amends for his "fried chicken" remark.
Garcia, playing in a three-ball with compatriot Gonzalo Fernandez-Castano and former world number one Luke Donald at Wentworth on Thursday, opened his campaign with a 72.
It was Garcia who received the loudest cheer from the gallery surrounding the first tee and he responded with a booming drive down the middle.
Three birdies in four holes to the seventh put the world number 14 in a good position. He then fell away on the back nine before grabbing the first eagle three at the 18th all day, an effort that prompted a huge roar from the crowd.