In the Feedback Vertex Set in Tournaments (FVST) problem, we are given a tournament T and a positive integer k. The objective is to determine whether there exists a vertex set X ⊆ V(T) of size at most k such that T-X is a directed acyclic graph. This problem is known to be equivalent to the problem of hitting all directed triangles, thereby using the best-known algorithm for the 3-Hitting Set problem results in an algorithm for FVST with a running time of 2.076^k ⋅ n^{(1)} [Wahlström, Ph.D. Thesis]. Kumar and Lokshtanov [STACS 2016] designed a more efficient algorithm with a running time of 1.6181^k ⋅ n^{(1)}. A generalization of FVST, called Subset-FVST, includes an additional subset S ⊆ V(T) in the input. The goal for Subset-FVST is to find a vertex set X ⊆ V(T) of size at most k such that T-X contains no directed cycles that pass through any vertex in S. This generalized problem can also be represented as a 3-Hitting Set problem, leading to a running time of 2.076^k ⋅ n^{(1)}. Bai and Xiao [Theoretical Computer Science 2023] improved this and obtained an algorithm with running time 2^{k + o(k)} ⋅ n^{(1)}. In our work, we extend the algorithm of Kumar and Lokshtanov [STACS 2016] to solve Subset-FVST, obtaining an algorithm with a running time {}(1.6181^k + n^{{}(1)}), matching the running time for FVST
