Equip Retainers with HQ gear

[MistakeNot]

Indirectly it could. As far as I can tell the only stat that matters for DoL retainers is their Gathering score - unlike DoW/DoM retainers where ilvl is what matters.
Higher gathering improves number of items gathered as well as the time needed - up to a limit. I do not know for sure if their Perception matters at all for the quality, or if that is based on their Gathering as well - I think it is all Gathering though.

So, if the HQ gear provides a better Gathering score than NQ gear would, then it would let the retainer improve their haul.

[Kenyon]

As far as I can tell the only stat that matters for DoL retainers is their Gathering score - unlike DoW/DoM retainers where ilvl is what matters.

You have answered a secondary question of mine about my Dragoon Retainer hunting Sea Swallow skins. Based on your answer I boosted my retainer from iLevel 413 to iLevel 450 (all HQ gear). This boosted the overall haul from 7 items to 10 items but made little difference to the number of HQ items. At 413 I was getting 2 out of 7 HQ and at 450 I was getting 2 (or 3) out of 10. Hence, I think iLevel affects HQ very little. On that basis I dropped my retainer to iLevel 431 gear which still provides 10 skins.