As far as I know, the only information which is available is the parent-child relationship
between cells.
mesh2.data().array("parent_cell", mesh2.topology().dim())
which is a list of cell indices in the original mesh. I guess you could use that to iterate through
the parent mesh, and work out how many children each cell has:
count = CellFunction("size_t", mesh, 0)
for idx in mesh2.data().array("parent_cell", mesh2.topology().dim()):
count[idx] += 1
Now you have a CellFunction on the original mesh. You can go through the new mesh,
and check the count for your parent... if it is more than 1, then it is a refined cell.