For sure you need to change ownership percentage and applicable consolidation method/scripts.
It completely depends on your application design and whether the change of control happens at the start of a new fiscal year or if it's within the year. I assume you have methods defined in the application along with the associated Sub Consolidate rules. There are two ways to assign methods: directly, or indirectly by calculating the method in the ownership management module. If you change methods for the parent.child relationship mid-year, you should perform a Periodic consolidation. But if methods change only at the start of a new fiscal year, you can use YTD consolidation. In either case you should not change this scenario setting unless you intend to reconsolidate and verify all of the history in the scenario.
If you do not have methods defined, it is possible to hard-code the relationship in Sub Consolidate, but that's a more involved exercise in configuring this than what we can do in this forum.