The EastEnders actress lost her place in the BBC contest after falling into the bottom two with Holly Valance and Artem Chigvintsev.
© BBC
Dobson danced the cha cha cha with Strictly professional Brendan Cole after her regular partner Robin Windsor was forced out with a foot infection.
On her absent companion, Dobson said: "He made this the most humorous, enjoyable, fun, wonderful learning experience you could ever imagine. Thank you so much."
She added to hosts Tess Daly and Claudia Winkleman: "Can I just say thank you to Brendan too, because without him I wouldn't have done this week… thank you."
Before taking her final dance, Dobson was surprised by a phone call from Windsor himself, who described the 62-year-old as "absolutely incredible".
"It has been a pleasure to work with you," he continued. "You have been one of the most enthusiastic and hard-working people I've ever, ever, ever met. I'm going to miss you dearly."
It has been announced that next week's quarter-final will have a 'movie night' theme.
Strictly Come Dancing returns Saturday, December 3 at 7pm on BBC One.
> Anita Dobson: 'I want to stay on Strictly Come Dancing forever'
Watch Anita Dobson on Strictly Come Dancing below:
