Do we need to add "a": In (a) modern society characterized?

In a dictionary, I found the following phrase: "in modern society"

But when I used it in the following way and get the check from website "grammarly.com", it said I needed to add "a" before modern. Why do we need to add "a" when I used characterized after society?

In modern society characterized by a swift lifestyle, people have experienced ever-increasing complex lives.

grammarly uses statistics to enhance their models, I'm pretty sure.

The idiom without article can be found frequently enough that it might distinguish certain uses following a basic grammatical model.

I guess the participle throws it off because indeed it sounds odd. And they might support this finding with syntactic models.

Abstract nouns, often characterized by adjectives, take an article; "modern society" does not, because it's treated as a compound noun. The participle does count as (a) adjective, therefore an article is needed. This is just a rule of thumb I think, but it's reasonable to mark the head of a longer noun phrase clearly as such. It helps parsing. (b) technically it is a participle phrase, but for sake of illustration consider in a green and evergrowing society. Removing the article does not work here either.

Also, you need two commas if you omit the article, so that you have two sentence adverbial phrases, basically as if people or have was characterized by .... But, that is probably not what you intended. The same could be however an unimportant paranthetical. It is not.

The characterization is vital, then, because you select one of a many different modern societies.

You don't need to add an "a." You should take grammarly.com or any other grammar correcting software with a grain of salt. Recognizing correct English grammar in all cases algorithmically is an unsolved problem. You should expect that sometimes the software will make incorrect or unnecessary suggestions and sometimes it will miss errors.

In fact it did miss that you should've written "ever increasingly." While it's not ungrammatical to write ever-increasing, it almost certainly doesn't mean what you want.