It is important to know (and is not clear from your description) whether you are an employee of the agency? If you are, then the answer to your question is that an employer cannot make deductions from your paycheck under California Labor Code sections 221-224, other than for a few itemized and statutory exceptions. (and what you mentioned is not one of them)
However, I assume from your description that you are not an employee of the agency like you would be for example at Kelly Services. But even then, it is also important to know who pays your check and whether/how the deduction of the money is taken from your check or whether you pay by writing a personal check to the agency? Even if you were not employed by the agency, your actual hiring employer still is limited to what it can deduct from your paycheck under California Labor Code 221/224. [In other words, the $150 cannot be automatically deducted from your payroll check by your employer, but you still may owe it to the agency]
Finally, lets assume that the agency is not your employer and that you send a personal check to the agency as payment. In such a situation, the employment agency works like a headhunter/recruiter and not as your employer and is paid on a contract basis for this service. Payment to the agency is made by either the hiring employer or the hired employee. It is for the most part based on the contract that was signed. But this analysis is very superficial without more facts. For example, there maybe a way to argue that the agency is also your employer. You should speak to an employment attorney and go over the above, and also allow him/her to inspect the contract that you signed with the employment agency.
I agree with Alex Sliheet (for a change!) The employer cannot deduct any amounts from your paycheck without written authorization, and the employer cannot force you to pay business expenses out of your paycheck. But if this is a contract for services, and you are paying separately from your paycheck, that is, of course, legal.
Pope, Berger & Williams, LLP