The authors compute a sophisticated average of German cities and compare the weighted number of positive SARS-CoV-2 tests to the city of Jena for a timespan of one month starting just before masks became obligatory there (6th April). Masks did not become obligatory elsewhere and roughly around the mask obligation new positive cases drastically reduced in Jena whereas the weighted average shows no such effect.
EDIT: moved my doubts in the study into extra comment.
If you think the summary is wrong, please leave a comment pointing out in which way, after downvoting.