  We present a $9^k\cdot n^{O(1)}$-time algorithm for the proper circular-arc
vertex deletion problem, resolving an open problem of van 't Hof and Villanger
[Algorithmica 2013] and Crespelle et al. [arXiv:2001.06867]. Our structural
study also implies parameterized algorithms for modification problems toward
proper Helly circular-arc graphs.
