Garcia was seven over par after just eight holes of his opening round at Merion, hitting consecutive tee shots out of bounds on the 14th and 15th to run up a double bogey and quadruple bogey respectively.
The Ryder Cup star also bogeyed the 18th but then birdied the first and eagled the second and, after another dropped shot on the fourth, birdied the eighth and 10th to card a three-over par 73.
He had been warned by Colin Montgomerie that he could be booed in the aftermath of his running feud with Woods, which took an ugly turn when Garcia was asked at an awards event last month if he would have Woods rounds to dinner this week to settle their differences.
"We'll have him round every night," Garcia responded. "We'll serve fried chicken."
The Spanish for fried chicken, 'pollo frito' was one of the things shouted at Garcia, but the 33-year-old wisely did not make an issue of it, with the Golf Channel reporting that he declined an offer from officials to have the hecklers removed.
"I think it was very good for the most part, I was happy with it," Garcia said of the reaction from the fans, some of whom had shouted 'Go get 'em Sergio' as he left the 11th tee.
"There were a couple (of wisecracks) but I thought the people were very nice. Almost all of them were behind me and that was nice."
As for his round, Garcia added: "I had two really bad holes but that's the way it is. This US Open is not giving you much room.
"On the 14th I slipped and hooked my drive out of bounds and on the 15th I hit a really bad tee shot out of bounds.
"I was making my week a bit tougher but I battled back as much as I could coming in and was able to shoot a decent score after being seven over after eight."
Garcia shook hands with Woods on the range on Monday and left a note in the world number one's locker on Tuesday after being unable to apologise in person, but has not seen him since.