How to optimize a mesh which I manually aligned

I manually aligned a mesh to another mesh. Two meshes have different topologies. The resulting mesh does not have a flat and smooth surface as is illustrated in the first picture.

My question is that, if there exist algorithms or tools such as a function inside meshlab or blender etc. that can smooth and optimize my mesh.

This is my mesh.

And I want to optimize it such that it is smooth like this:

I don't see the relation between "I manually aligned a mesh" and "resulting mesh does not have a flat and smooth surface". The aligned mesh should be similar to input mesh.

Despite that, try to apply the Meshlab filter Taubin Smooth to your mesh to rearrange the topology without introducing big deformations.