I'm assuming that you're an American Company (or company that does business in America)... Trademarks are territorial, and I'm not competent regarding international TM law (or some would probably say US law as well)...
You said:
"I have a store on a print of demand service, where I can put my designs or simple text on products such as shirts, cards, buttons and so on."
If I interpret your post correctly, the person clicks the link/button you provided at your website (the button including possible wording for a clothing item), and you provide an article of clothing (or the other items) having that particular verbage/wording ? If this is the case, it appears that you could have a problem...
Even if you don't manufacture/print the clothing items yourself, it would seem reasonable that selling the service to provide clothing to others with a protected mark could be considered confusing to a person (i.e., that you are associated with the actual owner of the mark used on clothing)...
If the words "Polka Dots" was a protected mark by Company A as used in conjunction with T-shirts, and you are selling T-Shirts with the words "Polka Dots" written on them, I would think it to be reasonable that a buyer could confuse you as being associated with Company A. Now if "Polka Dots" was protected as an extremely stylized design, and there were already several other renditions of "Polka Dots" verbage on T-Shirts prior to Company A use (or in some cases, since Company A's usage if the other instances have been around commercially for several years), and your use of "polka Dots" looked nothing like Company A's, then it might be OK... Really depends on the particulars of the situation...
And, it usually isn't a good idea to put your exact situation on the internet... That is why I spoke of only generalities in my post...
Good luck.
As mentioned above, there are many factors in a true likelihood of confuson test that need to be considered, so a simple 2 minuteslook will not do you justice...