  We study screening correlators of quark-antiquark composites at T=2T_c, where
T_c is the QCD phase transition temperature, using overlap quarks in the
quenched approximation of lattice QCD. As the lattice spacing is changed from
1/4T to a=1/6T and 1/8T, we find that screening correlators change little, in
contrast with the situation for other types of lattice fermions. All
correlators are close to the ideal gas prediction at small separations. The
long distance falloff is clearly exponential, showing that a parametrization by
a single screening length is possible at distances z > 1/T. The correlator
corresponding to the thermal vector is close to the ideal gas value at all
distances, whereas that for the thermal scalar deviates at large distances.
This is examined through the screening lengths and momentum space correlators.
There is strong evidence that the screening transfer matrix does not have
reflection positivity.
