The teenager made the comments just weeks after she appeared with her dad for her American Idol audition.
"my dad says more to our two dogs a day than he has said anything to me the past two years and his entire feed is bonnie and skipper but i support it," Claudia wrote.
The Sun has contacted the Lincoln Project for comment, but has not yet heard back.
The comments came just weeks after Claudia made it through her singing audition, and her parents, Kellyanne and George, made appearances.
George, of the anti-Trump Lincoln Project, was heard telling his daughter he was happy to see her on the show.
He then echoed his sentiments in a testimonial to the cameras, before wiping tears from his eyes.
Her mom appeared via video call to wish her daughter luck, asking "are you ready to go baby, are you excited?"
"This is your time to shine," Kellyanne said, "Remember honey, winners are people who are willing to lose."
Claudia returned to Twitter after a brief hiatus to tease her American Idol appearance – but not without slamming Trump's verdict in his second impeachment.
Back in January, Claudia released a video saying she would be "taking a break" from social media to work on her relationship with her mom.
It was following allegations that her mom, Kellyanne, had leaked a nude photograph of the teen on Twitter.
However, Claudia quickly debunked the claims and instead said she believes her mom was hacked.
"I have faith and I know that my mother would never put something like that on the internet," she said.
The Sun reached out to Kellyanne Conway and the Lincoln Project for comment on the allegations at the time, but did not hear back.
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