Board Thread:Skyrim/@comment-108.220.175.122-20150616212525/@comment-26103034-20150616213442

Because the Worn Shrouded Armour is terrible, you have to give her better armour (like Elven or normal Shrouded Armour) so she equips that. Then, dismiss her. Now pickpocket the default leather armour from her. Recruit her again and take the Elven or normal Shrouded Armour (or whatever) armour away via trade.

She will now be naked and you can give her any armour you want.

Hopefully this was clear enough and helps.