Take a look at any of the TTK weapons that were shown. None of them have an icon in the left column indicating they can be reforged. Just the infusion. It seems HoW weapons can still be reforged, but TTK weapons can't.
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Deej didnt have any TTK weapons equiped at the time. Reforging only works for equiped weapons.
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Yes, only equipped weapons will show up on the gunsmith's reforge list. But if you inspect an unequipped HoW weapon, you'll still see the 'Reforge Ready' perk. They inspected a TTK weapon, and only perk in that column was the infusion. So either TTK weapons can't be reforged, or they can all inherently be reforged even without the 'Reforge Ready' perk.