To comment on a claim, you need to hold at least Writer level rights in that discussion (see: Participant Rights and Roles). If you don’t have the permissions necessary to directly comment on claims in a discussion, you can still submit a suggested improvement - a comment initially only visible to Admins of a discussion. To suggest an improvement, follow the steps listed in Commenting on a Claim in any discussion in which you do not have participation rights.
Any Admin in the discussion can accept your suggested improvement, turning it into a standard comment in the comment log of the relevant claim. Admins can also respond to your suggested improvement, and you can edit and resubmit it if Admins do not initially accept it.