"People" or "the people"

There’s a very subtle difference. People on its own suggests that those in the list are there by chance. The people, on the other hand, suggests they been included deliberately. For practical purposes, however, it makes very little difference one way or the other.

People in the list

Can be replaced by

Subscribers to the list

Or simply

Subscribers

Assuming the context gives enough information about it being a mailing list, people should be able to figure out what it means.

In full:

Subscribers will also receive product update notifications. Please double check that the e-mail addresses are correct.