Delensing the Cosmic Background Radiation

You wouldn't expect much effect due on the amplitude (temperature) of the CMB due to gravitational lensing. The effect shows up in the polarization.

This has always been confusing, but here is how I understand it. The confusion is that electromagnetic radiation has an electrical component and a perpendicular magnetic component, but the description E-Mode and M-Mode do not refer to these.

E-Mode

A static electric field has field lines of force that originate on positive charges and end on negative charges and have no closed loops. A vector field that looks like this is an E-Mode vector field. Mathematically, there is divergence (on the charges) but curl=0 (no loops).

M-Mode

A static magnetic field has field lines of force that form closed loops with no end points. A vector field that looks like this is an M-Mode vector field. Mathematically, there is zero divergence (no magnetic charges) but nonzero curl (loops).

A general vector field will be the sum of an E-Mode and M-Mode vector field just as a general function is the sum of an even and odd function.

Electromagnetic fields consist of an electrical vector direction and a perpendicular magnetic vector direction. Shown below is an example of E-mode and B-mode, with the electric radiation vector on the top and the magnetic radiation vector on the bottom. Polarization direction is generally defined as the electric field direction. The polarization direction can be considered a vector field written on the sky.

B-mode polarization is considered evidence for gravitational waves whereas E-mode can be generated by other processes.

https://www.quora.com/Cosmic-Microwave-Background-What-are-B-modes

Gravitational lensing distorts the background as shown below as a distant galaxy is distorted into a ring shape, and this distortion can convert E-mode polarization direction vector field into B-mode, thus giving a false indication of gravity waves.

https://en.wikipedia.org/wiki/Gravitational_lens

Gravitational lensing by a black hole (simulation):