This is happening because text object, being a bezier curve of sorts, is filled with triangulated faces on the tops. You text object then seems to be curved backwards causing the triangulation to become visible.
It appears to be actually a problem of lack of subdivisions and bad topology.
This is one of the reasons quad based topology is always preferred, but in the case of bezier curves this is not possible without destructively converting it to mesh.
Make a copy of your text object if you haven't already (keep the original somewhere) and then try converting it to a mesh. Then either add a Subdivide modifier (this alone won't totally fix the problem) or manually remove all the top triangulated faces and try to fill them with a more uniform quad based grid where possible, or ideally do both, so the curve modifier has more geometry to operate on.
Only then on top of the fixed mesh apply your curve deformation.