Yes
Specific beats generalExceptions Supersede General Rules.
Exceptions Supersede General Rules
General rules govern each part of the game. A general rule is in effect as long as something in the game doesn’t explicitly say otherwise. When an exception and a general rule disagree, the exception wins.
The Grappled condition is more specific thanan exception to the rules for Mounted Combat because it applies in a narrower, triggered circumstance and explicitly grants an action, which mounted combat does not remove.
The Mounted Combat rules describe a general situation—how movement, initiative, and positioning work when one creature rides another. They do not restrict actions except where explicitly stated, and those restrictions apply to the mount’s normal actions.
By contrast, the Grappled condition is a defined mechanical state with explicit rules that apply only while the condition exists. Conditions are designed to override normal circumstances.
The Grappled condition explicitly grants a mechanical permission:
A grappled creature can use its action to make a Strength (Athletics) or Dexterity (Acrobatics) check against the grapple’s escape DC, ending the condition on itself on a success.
Because this permission is explicit and no mounted combat rule negates it, a grappled controlled mount may use its action to attempt to escape the grapple.