As M. Beckstette has kindly pointed out the following sentence can by misunderstood:
"We have implemented a C library using a data structure called enhanced suffix arrays (ESA). Using a modified version of the ESAsearch algorithm, introduced by Beckstette et al. [17], we are able to solve the scoring problem with a speedup of as much as a factor 1000 compared to a naïve implementation (see supplementary material, text S1)."
We do not claim that it is our modifications that gives this speed-up. Rather it is achieved by the use of enhanced suffix arrays. We apologize for any misunderstandings.