According to Roll Call,
Here’s the process: if a candidate contests the race before the committee, two majority members and one minority member investigate and then the committee recommends a course of action. That recommendation is voted on by the full panel and sent to the House floor for consideration just like any other bill that is reported out of a committee.
Because the Democrats do not take control of the House until Jan. 3, it is likely that any investigation by House Administration would be launched while Republicans are still in charge -- meaning the GOP will have the 2-1 majority on the investigating committee. But by the time the full House would be asked to seat the new Member, the Democrats would be in the majority.
Implications on the flip:
The committee would have 2 republicans on it and would not want a democratic winner or a revote. The committee would end up supporting the Republican as the ligitimate victor, with perhaps a nod toward needing better election protocols in the future.
When the new house votes, there will be pressure to a) support the declared winner and b) follow the recommendations of the House committee.
If the house votes to seat Jennings, the democrat, then there would be a lot of bad press for a few news cycles. I believe if it gets this far, the best option is to call for a revote. Note that there is precident in Florida for this to occur.