The ITV series, which is based on the format of French show Les Rencontres du Papotin, has seen the likes of David Tennant and Danny Dyer all quizzed by a group of autistic, neurodivergent and/or learning disabled interviewers.
When asked about the reaction to his comment on The Assembly, Lineker said it had been "completely blown out of proportion" and called the situation "very frustrating".
"It was a crazy week and it upset me," he added. "I had all the press outside my house every minute of the day, for about five/six days. It got a bit silly but it was actually also lovely because the backing I got from the people I work with was beautiful."
In the following days, it was announced that the dispute had been resolved, with Lineker re-instated and BBC Director General Tim Davie releasing a statement.
"That is a difficult balancing act to get right where people are subject to different contracts and on air positions, and with different audience and social media profiles."
Speaking on The Rest Is Football podcast, Lineker said of his decision to leave: "I think the thing to say is it's basically news of an extra year contract. I always thought my next thing would be the end, I've been thinking about it for a long time.
"I'll miss you [Shearer and Richards] but I'll still see you on the podcast regularly, that's for sure. But yeah, it felt like the right time. It came at point, really, where the BBC and Match of the Day got the rights for another three years. The cycle starts from next season, so it felt like if I just do one more year it would have been a bit weird.
The Assembly: Gary Lineker airs Sunday 11th May at 10pm on ITV1, ITVX, STV and STV Player. Stream from 7am on Sunday 11th May.
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