you'll have to make a user for each Windows group or specific login, the rest is the same you would do in any other database: create a role with only the minimal permissions to a handful of tables

USE msdb;

GO

CREATE ROLE MailReview

GRANT SELECT ON dbo.sysmail_sentitems TO MailReview;

GRANT SELECT ON dbo.sysmail_unsentitems TO MailReview;

GRANT SELECT ON dbo.sysmail_faileditems TO MailReview;

--a Windows Group login example

CREATE USER [mydomain\Developers] FOR LOGIN [mydomain\Developers];

EXEC sp_addrolemember 'MailReview','mydomain\Developers';

--a SQL login example

CREATE USER LOWELL FOR LOGIN LOWELL;

EXEC sp_addrolemember 'MailReview','LOWELL';