You have two way for your question :

1- Use Update Command in your Trigger.

ALTER TRIGGER [dbo].[tr_SCHEDULE_Modified]
   ON [dbo].[SCHEDULE]
   AFTER UPDATE
AS BEGIN
    SET NOCOUNT ON;
    IF UPDATE (QtyToRepair) 
    BEGIN
        UPDATE SCHEDULE 
        SET modified = GETDATE()
           , ModifiedUser = SUSER_NAME()
           , ModifiedHost = HOST_NAME()
        FROM SCHEDULE S INNER JOIN Inserted I 
        ON S.OrderNo = I.OrderNo and S.PartNumber = I.PartNumber
        WHERE S.QtyToRepair <> I.QtyToRepair
    END 
END

2- Use Join between Inserted table and deleted table

ALTER TRIGGER [dbo].[tr_SCHEDULE_Modified]
   ON [dbo].[SCHEDULE]
   AFTER UPDATE
AS BEGIN
    SET NOCOUNT ON;    

    UPDATE SCHEDULE 
    SET modified = GETDATE()
       , ModifiedUser = SUSER_NAME()
       , ModifiedHost = HOST_NAME()
    FROM SCHEDULE S 
    INNER JOIN Inserted I ON S.OrderNo = I.OrderNo and S.PartNumber = I.PartNumber
    INNER JOIN Deleted D ON S.OrderNo = D.OrderNo and S.PartNumber = D.PartNumber                  
    WHERE S.QtyToRepair <> I.QtyToRepair
    AND D.QtyToRepair <> I.QtyToRepair
END

When you use update command for table SCHEDULE and Set QtyToRepair Column to new value, if new value equal to old value in one or multi row, solution 1 update all updated row in Schedule table but solution 2 update only schedule rows that old value not equal to new value.