This Phase 2b/3 study is a randomized, controlled, multicenter, double-masked, parallel trial to compare the safety and efficacy of TP-03, 0.25%, to vehicle control for the treatment of Demodex blepharitis. The primary objective of the study is to assess the safety and efficacy of TP-03 compared to its vehicle from Day 1 to Day 43 in adult participants with mild to severe Demodex blepharitis. The primary efficacy endpoint will be cure based upon collarettes. Safety will be determined by assessing adverse effects related to the treatment as well as evaluating any changes in visual acuity, intraocular pressure, slit lamp biomicroscopy and dilated ophthalmoscopy findings.