How do TMMi based organizations benefit from the Agile way of thinking?

Within Agile test improvements will typically take place through an organization-wide Test Process Group that can take rapid action

By using TMMi as a reminder of critical testing practices that are often not defined or "forgotten" in Agile development methodologies

The Agile way of thinking typically brings out the initiative to further detail the test processes as they are currently defined

By only focusing on team-based related test process areas, and omitting anything that is related to improving testing at an organizational level.