Also known as Approaches in the code, they are called Phase/Detection groups on the Signal Configuration page. You cannot delete them if they have been used in the approach aggregation charts, and get Internal Server Error 500. The error is a database FK_Constraint on ApproachCycleAggregations, ApproachPcdAggregations, and ApproachSplitFailAggregations tables (Foreign Key: ApproachID).
The manual fix is to delete all the rows from the aggregation tables that contain the approach ID you are trying to delete.
This only matters if you are running aggregations in the first place. We wanted to document it here, but are unsure of the best fix- either database or code.