If not for the sake of the live in girlfriend, and husband they humiliated / betrayed publicly, then from a genuine sense of remorse and decency they should withdraw. If I was one of the show producers I'd be having a quiet word quite frankly. A 'do the honourable thing' type chat.
No one is going to vote for them after this anyway.
Footage of their rehearsals, any dance that has any kind of body contact / sexiness / emotional intensity, is going to be scrutinised and analysed and so on by the media and on social media. His jokes will fall flat, any attempt at playfulness, laughing and joking will seem forced and fake. I just don't see how they can possibly carry on in the show after this, anyway.
They will inevitably end up in the dance off against another couple, and imagine if they are saved and the other couple go? That's going to cause an outcry. They could end up in the dance off for the next several weeks, because they just aren't going to get the public votes to keep them out. Will the judges need to mark them up to keep them up? Then there will be complaints about bias and on it goes.
The damage is done, they've caused the damage, they are the ones who have got pissed up in public and behaved like idiots, and they would be doing themselves, their current and former husband / girlfriend .. and everyone else, a favour by calling it a day. I doubt he was that popular with the Strictly audience to start with, and any popularity he may have had, has gone straight down the crapper after this.