Legally speaking, there's no limit on the sanctions the House could arguably choose to impose, but that doesn't really answer your question. You're really asking what kinds of sanctions are appropriate in the circumstance of this case. That is a matter of judgment for the House ultimately to decide, although the committee may have thoughts on that.
My understanding of circumstances like these is that if the individual is found to have breached privilege or to have acted in a manner that's contemptuous of the House, the individual is given an opportunity to purge the contempt, as it were. That's usually done by an apology. If the apology is found to be genuine and complete, and there are no other lingering mala fides at issue, the House or the committee might be happy with that.
Now, do you want to go further and have a whipping, as it were, or whatever? What do you want to do? How much blood does the House need from any offending party before the matter has been adequately addressed? Your question is that open. It's not that the House can act irresponsibly; I don't mean to suggest that. I'm speaking rather carelessly here, but I'm speaking in this manner to illustrate the point that it's a very open question as to what is the appropriate action—very open. As public office holders, which you are, your judgment is better than mine as to what would be appropriate for an individual the House finds to have breached privileges of the House.
Typically, my view is usually some kind of an apology, maybe calling the person in front of the bar of the House to publicly do that apology, or maybe some other way. I think the judgment is generally that as long as the offence is redressed in some manner, adequately to indicate that the individual acknowledges what he or she did was not appropriate, then that probably is taken as a sufficient answer to the issue in most cases.