The phrase "despite its influence" is correct and usable in written English.
It can be used to indicate that something occurs or is true regardless of the influence of a particular factor.
Example: "Despite its influence, the policy did not achieve the desired outcomes."
Alternatives: "in spite of its impact" or "regardless of its effect".
Despite its influence, it closed after two seasons, though it staged occasional productions for another three years whenever a play Brahm deemed worthy was denied a public license.
Fantastic print design is not a relic of the past, despite its influence on today's designers.
Despite its influence on World War II, however, the memorandum ended up inside a South Carolina safe, nearly forgotten for more than a decade until a college student made it his senior thesis.
The entry for D&D on Wikipedia is twice the length of the article on Proust.But despite its influence on mainstream culture, D&D as a pastime is still a minority pursuit.
Despite its influence with Damascus and Hezbollah, the Lebanese Shia militia fighting alongside government forces, Iran has been largely excluded from international talks to forge a peace settlement owing to US and British objections that Tehran does not accept the need for Assad to quit.
Even then, and despite its influence among Hi-Tech architects, the geodesic dome remains a rare and exotic building type.
Despite this, its influence has grown both among the fringe right and more mainstream conservatives.
Despite its political influence, it poor economic development and administrative record, organised crime and corruption kept it amongst India's backward states.
Wijdeveld as the mouthpiece for the Amsterdam School of architects and designers, it is largely forgotten, despite its important influence on modern typography.
Despite its diminished influence, Piaget's theory continues to serve as a basis for other views.
Despite its persistent influence, the role of state media receives precious little attention from outsiders.
