You are probably protected because the storage center gains a statutory lien against the property contained in a storage unit.
However, you will want to chat with an attorney in your state to see if the statute carves out any exceptions. I doubt it, travelers checks are basically a near cash equivalent, almost like finding a $100 bill on the street. The person to whom they were issued can have them cancelled and refunded.
I agree that the traveler's checks are like cash and because you purchased the contents of the storage unit you are entitled to the contents.
This answer is for informational purposes only and may not be relied upon as legal advice.
Don't these take two signatures, one when they are purchased, and one when they are spent? How did you deposit them? Did you counter-sign them? Did the checks have any warranty language on them?
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