What will happen to the distorted space and time around a mass when it is converted into energy? Will it back to its original configuration (0 gravity)? Or space time oscillates? Or anything else
To answer this, lets use a single atom as an example. Essentially, the energy contained in that atom (bonds between the sub-atomic particles in the atoms nucleus) radiates away at the speed of light away when released, mostly in the form of Gamma radiation. the gravitational field would radiate out in exactly the same way, since mass is essentially energy stored in the bonds between the particles that make up the nucleus of the atom.
This means the mass really was just stored energy, which is released when those bonds break. It would cause a ripple in the gravitational field. Of course, there being nothing were the atom used to be, there's nothing to attract anything there.
There are several ways to convert mass into energy. The mass of a star e.g. decreases slowly due to nuclear fusion processes. In this case energy is radiated away which corresponds to a slight decrease of mass. As the mass of the star remains spherical symmetric during this process, so does its gravitational field and thus the spacetime around the star will not be distorted.
The complete conversion of mass into energy is possible by particle-antiparticle annihilation. Perform this process in a ideal box (withstanding the heat) the weight of the box will not change and neither does the spacetime.
Distortions of spacetime are caused by asymmetric processes (more technically if the mass quadrupole moment of a system changes over time) as during the merger of black holes, supernovae explosions and the like.