  In the recent article [Kopteva, N., Numer. Math., 137, 607--642 (2017)] the
author obtained residual-type a posteriori error estimates in the energy norm
for singularly perturbed semilinear reaction-diffusion equations on anisotropic
triangulations. The error constants in these estimates are independent of the
diameters and the aspect ratios of mesh elements and of the small perturbation
parameter. The purpose of this note is to improve the weights in the jump
residual part of the estimator. This is attained by using a novel sharper
version of the scaled trace theorem for anisotropic elements, in which the hat
basis functions are involved as weights.

Numerical Analysis;Numerical Analysis