Why is Grammarly marking my quotation marks?

Quotation marks used this way are commonly called scare quotes or shudder quotes. It’s a way of implying that you’re using a term in an unusual way or that you don’t necessarily approve of it.

How do I stop Grammarly from checking quotes?

You can adjust your document settings to stop Grammarly from checking text that appears inside quotation marks. At this time, this setting is available only in the Grammarly Editor. When you activate this setting, Grammarly will not make spelling or grammar suggestions for quoted text.