In my opinion, the committee first presents a report to the House about the case. If the committee's report proves the facts, a motion can be introduced in the House indicating that the minister, or prime minister, is found to be in contempt of Parliament and the House no longer has confidence in the government. It would be a motion like that. If the House of Commons supports that, it is a matter of confidence in the government.
Aside from that, I think it is difficult to find other legal or punitive means to make the government comply with the order of the committee.