NEC requires the going and returning current to be in the same wire bundle (cable or conduit), so the magnetic fields thrown off by the current in the wires cancel each other, thus preventing magnetically inducing current flow in adjacent metal objects, which could cause heating in the adjacent objects and possibly fires.
Power comes in on one or the other of the T travelers, goes through the 3-way switch to the common screw C then to the black L to the light, then returns on the white L from the light to the white in the traveler bundle. Magnetic fields are balanced in the LL cable and in the TNT cable.
The left side is goodThe left side is good, you don't need to adjust it, except to take out the right side's neutral.
The right side is problematic. It looks to me like someone wanted a light that only had one switch controlling it to have two switches in a 3-way arrangement, and wired the light wrongillegally to achieve this goal.