Harry did not react right away, as he was viewing the memory alone:
“Snape!” he shouted. “Severus Snape!”
“Snape has been cleared by this council,” said Crouch disdainfully. “He has been vouched for by Albus
Dumbledore.”
“No!” shouted Karkaroff, straining at the chains that bound him to the chair. “I assure you! Severus Snape is a Death
Eater!”
Dumbledore had gotten to his feet.
“I have given evidence already on this matter,” he said calmly. “Severus Snape was indeed a Death Eater. However,
he rejoined our side before Lord Voldemort’s downfall and turned spy for us, at great personal risk. He is now no
more a Death Eater than I am.”
Harry turned to look at Mad-Eye Moody. He was wearing a look of deep skepticism behind Dumbledore’s back.
There was too much going on in the memory to be distracted, probably Harry had suspected this turn of events. After viewing the Pensieve memories, having been interrupted by Dumbledore, Harry raises the question and gets an answer:
... “No more has Professor Snape,” he said.
Harry looked into Dumbledore’s light blue eyes, and the thing he really wanted to know spilled out of his mouth
before he could stop it.
“What made you think he’d really stopped supporting Voldemort, Professor?”
Dumbledore held Harry’s gaze for a few seconds, and then said, “That, Harry, is a matter between Professor Snape
and myself.”
Harry knew that the interview was over; Dumbledore did not look angry, yet there was a finality in his tone that told
Harry it was time to go. He stood up, and so did Dumbledore.
Harry did not question authority of Dumbledore before the events of OotP. He was probably convinced by the answer he got.