If the question is about what is grammatically "correct," I feel like the linked Grammarly article is clear:
When choosing between there is and there are, you have to look at what comes after the phrase:
Example: There is a cat on the porch
In the sentence above, cat is the subject, and since it is singular, it requires there is.
Example: There are many opportunities to learn at this company.
In the sentence above, opportunities is the subject, and since it is plural, it requires there are.
In your example sentence, marks is plural. You should use there are.
But since this is so clear, the rest of your question seems to be: Don't we hear people talk this way? Don't we hear "there is" even with plural subjects? Yes. This is where "grammatically correct" and "commonly used" aren't always the same thing. I could imagine someone saying "There is marks all over this floor." It would be a very informal way of speaking, and perhaps even associated with certain regions or groups of people. Personally I wouldn't say it; it wouldn't feel natural for me, not belonging to those groups. It would certainly feel out of place in writing (aside from the most informal writing like text messages). And I wouldn't advise an English learner to try it, especially since saying "There are marks all over this floor" would not sound unnatural or unwelcome in most contexts. (Unlike some other "grammar rules" that are so often broken that it might sound odd to stick to the "right" way.)
If the verb and subject have a few more words between them, the mismatch becomes less obvious. For instance, "There's a lot of people here today" doesn't sound quite so colloquial, and I say things like that myself often enough.