INSERT INTO MyTable (
       Col1
      ,Col2 )
OUTPUT DISTINCT -- issue is with DISTINCT
       INSERTED.Col1
      ,@otherParameter
       INTO IdListTable
SELECT ColA
      ,ColB
      ,SUM(ImportantNumber)
FROM MyOtherTable
GROUP BY ColA, ColB

INSERT INTO MyTable (
       Col1,
       Col2 )
OUTPUT
       INSERTED.Col1,
       @otherParameter
       INTO #tempIdListTable
SELECT ColA,
       ColB,
       SUM(ImportantNumber)
FROM MyOtherTable
GROUP BY ColA, ColB

Insert into IdListTable
Select distinct col1, col2 from #tempIdListTable