No. Presentation does not change the actual work, ownership or legal relationship.
Assess the real condition
Paying for a revised letter cannot cure facts that remain unchanged.
Costs vary by how many open questions remain: a credential evaluation, translation, dependent applications, and legal review of a genuinely ambiguous profession match all add scope beyond a straightforward case. Government charges for this category are modest compared with the categories that require petitions, but the exact amounts depend on whether the request is made at a port of entry or through an employer petition, and they are revised from time to time. Budget separately for citizenship records, the listed profession's credential evidence, any needed evaluation or translation, employer-letter preparation, advice, travel, and current government charges. If the employer is requesting the travel, ask in writing whether it covers changed flights, extended accommodation, and legal fees should the return be delayed or a new filing become necessary. Government charges apply according to the route taken and should be confirmed through official sources, since those amounts are set independently of any employer arrangement. A CBP admission request and an employer-filed USCIS petition involve different government charges, preparation time, and evidence presentation, while neither charge replaces the need for a qualifying position.