Clark says she found the invite and the accompanying blog post with a kitesurfing photo showing a naked model clinging to Branson's back, disrespectful.
She shot back with a one-liner of her own, saying if that's his best pick up line, there may be a reason he calls his company Virgin Group.
Clark met Branson last week after his airline company Virgin Atlantic made its inaugural flight from London to Vancouver.
Branson's blog says he asked the "delightful" Clark to kite surf while riding on his back.
Clark's office issued a written statement earlier, saying Branson is well-known for his brashness and ability to generate media coverage.
Also on HuffPost