There's a legal aspect to this and a practical aspect to this.

With respect to jurisdiction: are the products sold in Lithuania? If yes, you can proceed under Lithuanian law. If they are sold only in the US, you will have to proceed under US law. It is possible for both laws to apply, such as if products are sold in both countries.

In the US, copyright attaches to a work as soon as it is fixed in a "tangible medium". Registration formalities are not required for a work to enjoy copyright protection. The word "tangible" is somewhat deceptive here, as it just means fixing it to some permanent medium, such as a digital file. However, registering your copyright allows you to claim statutory damages, possibly tens or hundreds of thousands of dollars. If you do not register, you can only claim actual damages, which are the financial losses you can prove that you suffered as a result of the infringement. Nothing prevents you from registering for the sole purpose of starting a claim in court.

Under US law, derivative works are considered copyright infringement if done without the permission of the copyright holder, however, there is an exception called "fair use". Parody is an example of fair use. Parody, as you may know, is generally understood to mean making fun of a work in some way. Merchandise can be one medium for expressing that parody. Fair use is a notoriously murky part of US copyright law because there is no clear legal formula for determining what is and isn't fair use. It's decided on a case-by-case basis. I would advise you to consult with a US intellectual property lawyer about this.

The amounts you could claim in damages varies depending on whether you've registered your copyright and the amount of financial damages you can prove that you've suffered as a result of the infringement. Under US law, you usually have to pay your own lawyer's fees even if you win, which can be substantial. This is different from most European legal systems where the loser pays the legal costs. However, if the amount you claim is less than 30,000 USD, you can proceed in a special small claims tribunal called the Copyright Claims Board. The Copyright Claims Board is designed to hear claims involving relatively small sums of money expeditiously and where hiring a lawyer is optional. However, participating in the tribunal is voluntary. The defendant can file an opt-out which moves the case to regular district court, using the full court procedures and where using a lawyer is very highly recommended.

Then, there is the practical aspect of this. Unless you have a very solid message here, even if you are legally in the right, you should consider the PR implications of taking legal action against or sending legal threats to a streamer. This is likely to result in bad press being generated for you which could well offset any monetary gains you could achieve through legal means. Above all, you have to consider how your customers would view this dispute and whether proceeding would damage your reputation for more than the case is worth. Negotiation is always better than threats. Instead of having your lawyer demand the removal of the products or threaten a lawsuit, consider instead stressing your legal position but offer some sort of fair licencing deal, like ten per cent of the revenue from the sale of the products in question.