An additional pancake-antipancake vortex pair is considered in the vor
tex lattice of layered superconductors. Within linear elastic continuu
m theory, the relaxation of the background lattice screens the long-ra
nge logarithmic interaction of the defect pair, reducing the factor ln
(r(0)/xi) to In(a/epsilon) where r(0) is the pair spacing, xi the in-p
lane coherence length, and a the vortex spacing. The finite tilt modul
us does not destroy this ideal two-dimensional screening, yielding a s
mall correction similar to(a(2)/8 pi lambda(2))ln(r(0)/a), which in pr
inciple is of long range, but has a very small prefactor when the vort
ex spacing a is smaller than the in-plane penetration depth lambda.