Hi - my name is XXXXX XXXXX X'm an Intellectual Property litigation attorney here to assist you.
This certainly should not be a trademark issue because those claims only pertain to a specific mark or name/phrase (like the Nike Swoosh, or the McDonald's golden arches) or some other symbol that you were using that looked similar to theirs and could confuse the public or consumers that you were the other company.
There could be a copyright or patent claim if your product is exactly the same as the other one. However, if these are handmade, there's really no likelihood that you have infringed on a copyright - no more than you could claim a copyright infringement against the other company.
A company can't corner the market and be the only one in the world that produces a certain item, product, etc. (a good example is Coke v. Pepsi).
I would recommend that you have an attorney review the threats from these people and respond with a letter indicating that this is not a trademark.
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