Hi,
I had a look to the send grid documentation for their API:
sendgrid.com/.../
Seems like we can tread this as any 3rd party API call from Dynamics.
One solution for you would be to implement a Dynamics Action, from which you can send an HTTP request to this API (POST request) and send in the body the information about the email, contacts, etc.
This can also be achieved with JS, but now it will depend on your business requirement.
In other words, there is no native integration that I'm aware between Dynamics 365 and this software, but you can leverage any Dynamics 365 functionality that allows you to send an HTTP request to integrate with the send grid API.
Have a look to this thread: community.dynamics.com/.../how-to-call-3rd-party-api-from-dynamics-365-online
A lot of cool suggestions here, maybe something that better suits your needs :)
Thank you.