We present a method to selectively suppress unwanted higher-order resonances in all-dielectric tri-layer structural color filters, achieving reflective red (R), green (G), and blue (B) colors through controlled optical interference. By applying a gradient-based optimization technique, we fine-tune the designs to improve color purity by eliminating undesired resonances outside the passband of the tri-layer structure. The filters are composed of a low-refractive-index (LRI) layer sandwiched between two high-refractive-index (HRI) layers. Higher-order modes in the HRI layers and the fundamental mode in the LRI layer are exploited to generate B and G colors. For the R color, the reverse configuration is used: the HRI layers employ the fundamental mode, and the LRI layer operates in a higher-order mode, which introduces an unwanted peak at λ = 450 nm, significantly affecting color purity. To address this, we reduce the LRI thickness to half of the quarter-wave thickness (QWT) and increase the HRI thickness to a quarter of the QWT, shifting interference from constructive to destructive at λ = 450 nm while preserving constructive interference at λ = 642 nm. This effectively suppresses the higher-order mode, resulting in a pure R color. Our study provides valuable insights into the optical design of multilayer thin-film structures, with potential applications in reflective displays, image sensors, and colored solar cells.