The damage was discovered after the insured completed his work and so exclusions j5 and j6 are not applicable as neither of these exclusions apply to completed operations.

What you have to consider is the damage to your work exclusion, since this applies to completed operations. This exclusion applies to damage to the insured's work and not to damage to another's property that the insured's work causes. The insured's work was installing new gutters and downspouts. If there was damage to the gutters and downspouts, that would not be covered. But it seems here that the insured's work damaged the insulation and so, that would be covered. In order to repair the insulation, if peeling back the roof is required for the repair, this is covered also.