Grant Thompson, the 14-year-old who found Apple's FaceTime flaw, may get a bounty for his discovery.

"I kind of found this one on accident, which is pretty surprising to me that like Apple didn't get this and a 14-year-old kid found it by accident," Thompson told CNBC on Monday in an interview while sitting next to his mother. "A few of my friends know it and think it's pretty cool."

Grant's mother, Michele Thompson, said she repeatedly and unsuccessfully tried to contact Apple to report what her son found on Jan. 19 while putting together a group FaceTime with friends playing "Fortnite." She said the attempts included emails, tweets and Facebook posts.

"I didn't hear from [Apple] until after the media broke the story one week ago today," she said, referring to the report about the bug on tech site 9to5Mac that went viral.

She said a high-level Apple executive flew to Tucson, Arizona, on Friday afternoon to meet with Grant. The executive, whom she declined to name, "thanked us in person and also asked for our feedback, asked us how they could improve their reporting process."

"They also indicated that Grant would be eligible for the bug bounty program. And we would hear from their security team the following week in terms of what that meant," she said. "If he got some kind of bug bounty for what he found, we'd certainly put it to good use for his college because I think he's going to go far, hopefully. This is actually a field he was interested in before and even more so now."

Despite this experience, Grant Thompson said on "Squawk Box" that he will still use Apple products. "Every now and then something like this just falls through the cracks and can be found." He added he believes Apple is trying to protect user privacy.

On Friday, Apple apologized for the group FaceTime flaw that lets users hear through someone else's iPhone, even if they have not actually answered the phone call. The statement from the company thanked "the Thompson family for reporting the bug." Apple has disabled group FaceTime as a temporary fix, and promised a more permanent solution would roll out in a software update this week.

According to NBC News, the journalist who wrote last Monday's 9to5Mac story about the FaceTime bug said he saw Michele Thompson's tweet after his article was published, but she did not contribute to his reporting.

The FaceTime bug comes at a time when more and more questions are being asked about online privacy and Apple CEO Tim Cook has positioned the company as a champion of data protection. A day after the 9to5Mac report, Apple reported fiscal first quarter earnings and revenue that slightly beat estimates, but with a 15 percent drop in iPhone sales from the same period last year.