During 2022/2023 the optimal inefficiency of the Veto system of the SND@LHC detector was measured to be (7.8 ± 2.8) × 10−8. To reduce this inefficiency, a third Veto plane was installed during the 2023-2024 Year End Technical Stop. In addition, the Veto system was lowered to cover the target fully, thereby increasing acceptance. This paper describes how the inefficiency of the Veto system was reduced from (7.8 ± 2.8) × 10−8 with an acceptance of about 64% of the target area in 2022–2023 to (4.9 ± 1.9) × 10−9 on the full area in 2024.