  Hochschild cohomology is crucial for understanding deformation theory. In
arXiv:2304.10223, we have computed the Hochschild cohomology for gentle
algebras of punctured surfaces. The construction of that paper is rather
implicit and fails if the punctured surface has only a single puncture. In the
present note, we supplement the earlier method by providing an explicit
construction of Hochschild cocycles which also succeeds in the case of a single
puncture.
