Arguably, the word has no legal significance other than to place on the record the reluctance of a person who takes some legal action, such as paying a fine under protest.
A statement of something done under protest is significantly different to the qualification of something done without prejudice, as the latter does have legal significance.
As to the legal insignificance of under protest, in the 1845 case of In re Massey, a creditor of an estate accepted a payment under protest. The London, England Court wrote:
"The receipt (was) given under protest. These words are often used on these occasions but they have no distinct technical meaning .... unless explained by the proceedings and circumstances."
In Castano v Gabriel, New York City judge Wahl wrote:
"The naked assertion of under protest ... is merely an assertion that what is being done is contrary to the desire or intent of the protesting party.
"There is no magic in the term under protest."
However, in The Queen v Premier Mouton, the corporate taxpayer paid its taxes under protest. In a dissenting reasons, Justice Abbot wrote that under protest:
"... implied a reservation by (the taxpayer) of its right to claim repayment of the amounts paid."
The nebulous import of the term arose in R v Talbot where Mr. Talbot paid his motor vehicle violation ticket using the words under protest. This caused Justice Martin of the British Columbia Court of Appeal to adopt these words:
Under protest is an improper expression because fines cannot be paid in that way; they are paid or they are not paid.
"It is a growing practice which should be sharply discountenanced."
French: sous protêt.