NYTimes.com Terms Policy

The NYTimes pop-up message/prompt is not an ad.

But, when it shows, you could try to BLOCK the element and thereby store a custom filter at:

brave://settings/shields/filters


How to . . .

https://support.brave.com/hc/en-us/articles/360018039072-How-do-I-use-the-Content-Filter-to-block-elements-on-a-webpage