I'm thinking this has to be one of the easiest investigator weaknesses to deal with in the entire game, short of the ones you can afford to outright ignore sometimes. Most of the cards that help Trish deal with this weakness are cards she would have strongly considered running anyway.
Narrow Escape is already fantastic for Trish, this weakness practically makes it a cornerstone.
Obfuscation also helps with this and slides right into a completely uncontested slot (arcane). Since it's Fast, she can hold onto it until she needs it.
Cryptographic Cipher helps as well. Despite making the resulting investigate slightly tougher, at any 1 or 2 shroud location it's hardly noticeable and it lets her grab a clue AND discard her weakness without spending a single action. If it's sitting in her hand she could always Sleight of Hand it out as well...
Shortcut helps her position herself on top of a clue if she draws into this weakness at a location with 0 clues.
...and if there are no clues around you could always stoop to the level of more mortal investigators and simply spend an action to evade it and poof, it's gone.
Pretty cool. Trish seems extremely hard to slow down.