Generally, no, the fees are not deductible. The green card is a travel document and it is proof of lawful permanent residency status.
Below is a good explanation of why it generally is not deductible: https://forum.mrmoneymustache.com/taxes/are-feesexpenses-for-renewing-greencard-tax-deductible/
One thing you have to understand about the law is that unless the statute very clearly and explicitly addresses an issue, there might not be a simple "yes" or "no" answer. Instead, there might be possibly meritorious arguments on both sides. In the US, legal writers refers to possibly meritorious arguments as "colourable" arguments, although in Canada that term means something completely different. In Canada, something is "colourable" if its true purpose is different from what it appears on its face. For example, in R. v. Morgentaler, [1993] 3 SCR 463, the Supreme Court of Canada found that impugned provincial health legislation was really a colourable attempt to impermissibly regulate abortion, and was hence unconstitutional.
26 USC § 212 authorizes a miscellaneous itemized deduction for "ordinary and necessary expenses paid or incurred ... for the production or collection of income", subject to the 2% of AGI floor discussed by me in a previous post. Most likely the 2% floor is fatal to you, so you can't get any tax benefit from this fee and you don't need to analyse the problem further. If, however, the floor is not fatal, you need to consider whether the expense to renew your lawful permanent residency card ("green card") meets the test of 26 USC § 212 or some other statutory deduction.
The green card is a travel document and it is proof of lawful permanent residency status. However, it's the lawful permanent residency status that authorises you to work, not the card evidencing same. Even if the card is not renewed and is allowed to expire, you still remain authorised to work in the USA, although you could be arrested at any time for noncompliance with 8 USC § 1304, which is a misdemeanour punishable by a $100 fine and 30 days in jail. In some hypertechnical sense, the green card renewal is not required to work, but merely to avoid arrest, though perhaps you could argue that expenses to avoid arrest and conviction still meet the test of 26 USC § 212.
Ultimately, you and you alone have to decide whether you feel you have a persuasive argument for taking a deduction. I propose the following rule of thumb: only take a legal position if you are willing and able to defend it. If you don't feel up to task of defending the position if challenged, do not take the position. In this post, I have intended to provide you with some general information to start your research, but I am not providing any advice about what to do, because you are the one who has to make that decision.
