If you measure the speed of light using the Schwarzschild coordinates then you will calculate a speed that is less than $c$ when the light passes near a massive body. In this sense gravity does slow light. There are already several questions hereabouts that discuss this.

The issue tends to be a bit controversial because there are differing interpretations of what happens. An observer making a local measurement, that is measuring the speed of light at their location, will always measure the speed to be $c$. The distant observer gets a different value because the coordinate systems of the distant and local observer do not match.

Anyhow, the light does exert a force on the massive body. If you shine a laser close to the Sun, so it is deflected by gravitational lensing, then the momentum of the Sun changes by an equal and opposite amount to the momentum of the light beam. The change is far to small to be measurable, but it is there.

However things are a little more complicated than this. The laser beam does not exert a force on the Sun directly. The light is responding to the local curvature of spacetime. In doing so it changes that curvature very slightly, and that change propagates through spacetime to the Sun where it causes the Sun to accelerate. The mechanism is the same as a massive body being deflected by the Sun's gravitational field.

If you measure the speed of light using the Schwarzschild coordinates then you will calculate a speed that is less than $c$ when the light passes near a massive body. In this sense gravity does slow light. There are already several questions hereabouts that discuss this.

The issue tends to be a bit controversial because there are differing interpretations of what happens. An observer making a local measurement, that is measuring the speed of light at their location, will always measure the speed to be $c$. The distant observer gets a different value because the coordinate systems of the distant and local observer do not match.

Anyhow, the light does exert a force on the massive body. If you shine a laser close to the Sun, so it is deflected by gravitational lensing, then the momentum of the Sun changes by an equal and opposite amount to the momentum of the light beam. The change is far to small to be measurable, but it is there.

However things are a little more complicated than this. The laser beam does not exert a force on the Sun directly. The light is responding to the local curvature of spacetime. In doing so it changes that curvature very slightly, and that change propagates through spacetime to the Sun where it causes the Sun to accelerate. The mechanism is the same as a massive body being deflected by the Sun's gravitational field.