We received an invoice to pay publication fees for our applied mark. Do I have to pay it?

NO. If you have received such a document, you have most likely (already) settled your fees or was paid by your agent/attorney. In any case, remember that the competent offices DO NOT ISSUE INVOICES for the said fees. Most likely, you received the offer due to the publication of your trademark in the Official website/newsletter which includes information about the owner. You can read more about these missleading invoices here: MISLEADING INVOICES AND HOW TO RECOGNIZE THEM.