I was intrigued (initially) by Grammerly, but found it too lightweight to be of much use (back when it was first released). I went back and tried again when they released the next version, but again, it's not really a major contender in the 'writing tools' market.
That said, I too was worried about the phrasing. In most cases, it's largely innocent. The use covers sending the text to the cloud, where the site's owners can download, analyze and disburse necessary stats or examples. However, the language is so loosey-goosey they could decide to sell it as their own "Grammerly" novel and you wouldn't have a leg to stand on. (Who do you think a 3rd party arbitrator paid by Grammerly is going to side you? You, an unknown author, or the people paying their salary?)
We've discussed these issues with other sites. Ernest, in particular, won't have anything to do with Amazon based on their legal qualification (mostly concerning their ability to continue offering your work to those who've purchased your books once you've pulled you books and left the site), but the rest of us trust they won't go after individual authors for fear of the angry push back it would invoke. (There are enough people who already despise Amazon for their fight with the publishers a couple years ago.)
In this case, I'd guide you away from Grammerly. They might mean well, but given the "We retain all rights to any damn thing we want", and the lack of anything to be gained by using their service, I wouldn't bother.
For those unfamiliar, Grammerly is an online spell-checker for Macs that intercepts your typing, sending everything typed to the cloud to return spelling in documents/emails/messaging apps and other programs. As such, they're legally entitled to read anything and everything you type on your computer.