It appears that the other party has served you with a “Cease and Desist and Takedown” Letter reserving their rights under their registered trademark. The two products must be sufficiently similar that they would cause a risk of confusion in the minds of an onlooker. The trademark owner does not have to prove intention to copy, only that the two designs are similar and theirs is protected by trademark and was registered first.
Unfortunately, I believe that you will have to remove the other party's work from your website.
Registering a piece of Intellectual Property as a Patent, Trademark or Design Right means that it is automatically protected from all other similar designs and the Right Holder does not have to prove deliberate copying by the other party.
Therefore, any argument by you that you came up with the design first will not succeed. You should have registered it as a trademark to gain protection.
Damages for Intellectual Property Rights Infringement Claims are account of profits to the claimant for monies obtained through use of the mark.
You have two options.
You can either continue to use the design and risk the claimant issuing proceedings for a court injunction ordering you to remove the offending material, plus damages, interest, and costs.
Or you can remove the offending material and sign an undertaking not to use it in future.