The pair, who had been quarantining after contracting breakthrough cases of COVID-19, returned for Monday's episode of Dancing with the Stars to compete as part of "Disney Heroes" night, taking on the jive to "Stand Out" from A Goofy Movie.
When asked by host Tyra Banks if they were feeling the pressure, Rigsby, 34, replied, "No, I feel great! I'm so glad to be done with quarantine, I'm glad to be back in this space."
"I'm so obsessed with this look, this hair, this woman!" he added, pointing to Burke, 37.
The duo, who earned a score of 27 out of 40 from the judges, will also have a second chance to perform on Tuesday during this week's two-night Disney event.
Two days earlier, she announced that she had completed quarantine and would be dancing live with Rigsby during the upcoming episodes of DWTS.
"I have been officially cleared. I am back to normal. No more quarantine for me," she said on Instagram. "Unfortunately, Cody is still in quarantine, but he will be back in Los Angeles starting Friday, which means we can technically dance on both Monday and Tuesday."
Burke continued, "I'm grateful that we're healthy. Thank you guys for all your support over the past week-and-a-half or ten days. It's been truly an emotional rollercoaster, but wouldn't have been able to get through it without all of you guys and all of your support. I am just happy that Cody is okay, and we're still rehearsing via Zoom as we speak."
During last week's show, Burke and Rigsby gave DWTS' first-ever remote performance, filming their "Gimme More" jazz routine separately from their homes. Following the performance, Burke told PEOPLE the remote dance was "one of the hardest things" she has ever done.
"I'm just really grateful that despite everything that's happened in the last several days, we've been able to pivot and stay in the competition virtually for this week," she said.
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The pair received an 18 out of 30 for the routine, marking the lowest score that night. During an episode of her Pretty Messed Up podcast the next day, Burke said she and Rigsby "kind of got screwed by the judges."
"We basically have only gotten sixes since we started Dancing with the Stars, which is fine, I get it, but I think what I was looking for was a little bit of acknowledgement of what we did in order to make this whole production work," she explained.
"You don't have to talk about us getting COVID, we get it, we're sick, but at the end of the day, just the amount of work and having to dance as two soloists as opposed to dancing together, when you can manipulate your partner's body movement and the musicality," she added, noting that Rigsby deserved "extra credit" for the remote dance.
Dancing with the Stars airs Mondays on ABC.