How do galaxy clusters perturb the CMBR? It's through a process physicists call Compton scattering. To understand how how Compton scattering works it's helpful to understand some basics about radio waves. Radio and light are the same thing --electromagnetic radiation -- radio waves simply have a longer wavelength than light. Both come in packets called photons. One of the great advances of modern physics earlier this century was the realization that photons can act like waves and like particles at the same time. We are free to visualize a photon either way -- the physics is still the same.
  In this case, the easiest way to understand Compton scattering is to visualize a photon as a particle of light. When photons from the cosmic microwave background fly through the atmosphere of a galaxy cluster they collide with electrons in the hot gas. What happens then? It's similar to a game of pool. When one billiard ball collides with another they often careen away in unexpected, seemingly random directions (depending on one's skill as a pool player), and the two balls can exchange energy. The slower moving ball before the collision may become the faster moving one afterwards. It all depends on the exact details of the collision.
  When a photon whizzes through the cluster atmosphere much the same thing happens. The photon stands a good chance of colliding with an electrons (represented by an e^- symbol in the diagram at right). The two particles hit and rebound in new, random directions. The photon may gain or lose energy, once again depending on the detail of the collision. These collisions between photons and electrons are called "Compton scattering."

The effect of Compton scattering is really very small. Carlstrom and Joy use radio interferometers to observe photons with wavelengths near 1 centimeter. When such a photon passes through a cluster atmosphere, its typical energy gain due to Compton scattering is a miniscule 0.05%. Nevertheless, this tiny change is significant. When Carlstrom & Joy point their radio interferometer in the direction of a galaxy cluster, they see a deficit of CMBR photons. The "missing" photons were shifted, on average, to higher energy by Compton scattering.