So, instead of weapon that are like, "You gain this benefit if you have the Absolute's Mark," it would be something more like, "You are required to call upon the tadpole in order to use this item's powers.". So, item grants you a +1 to hit and damage with 1d6 extra whatever damage, or something similar, but only if you accept the tadpole's power. Once per day but affect lasts until long rest or weapon unequipped.
There's actually a perfect mechanic that they could retrofit to make an adaptation for for this, incidentally. If you read up on illithids, you'll find reference to the weapons and armours their thralls use. they're special magical/psionic equipment that is brutally powerful for its challenge bracket, but is made so by the illithid, specifically for use by their personal thralls to be effective with, and can't be utilised any other way. They could definitely do something to adapt that in a satisfying way, if they wanted to.
