The gradient paint filter applies a linear gradient paint: if acyclic it will from the first to second colour as it moves from the first point to the second point (points dependent on the direction of the paint which can be synchronised with the reflection direction or specified specially). If cyclic it will alternate between the two colours as it moves from point A to point B (same rule applies). This is what the UI looks like to begin with:

If you Apply before reflection the entire painted image will be reflected; otherwise if reflection filter is disabled this does not matter. If however you do not apply before reflection the reflection part of the image will be painted.

If you tick Cyclic Gradient Paint it makes the gradient paint cyclic, which I explained above.

The Paint direction I also already explained; if you Sync direction with reflection whatever the reflection direction is is what direction the paint will flow.

However if you Invert opacity the direction of the paint is reversed and the paint is darker, moving in the opposite direction.

The first and second paint colours are as I already explained the colours that make the gradient paint; the default colours are shown: if you Reset one it sets it back to the default; if you Reset both both are reset and if you Swap colours the colours are swapped.

The paint ratio and opacity are hard to explain but they affect each other as well as the darkness.

This is what the default looks like on a reflected image with acyclic paint:

If opacity is inverted, this is what it looks like:

This is how it looks if you paint before the reflection:

If you paint before the reflection with inverted opacity:

Finally if you make the paint cyclic this is what it looks like with the defaults: that is paint the reflection and not inverting the opacity: