Content-Aware Fill in this workflow belongs to After Effects. You need access to that application and compatible installations for Dynamic Link. Save a copy before replacing a timeline clip.
Send a short shot to After Effects
In Premiere, select the relevant clip and use Replace With After Effects Composition from its context menu, then save the After Effects project. Work on one continuous shot rather than a caption strip spanning unrelated cuts.
Create a transparent target area
In After Effects, mask the words and their shadow, set the mask to Subtract, and animate the mask path if necessary. Check that the transparent region covers the lettering throughout. Open Window → Content-Aware Fill.
Generate and inspect the fill
Choose a suitable Fill Method and Range, then Generate Fill Layer. Review the reconstructed region in motion. If texture or lighting fails, Adobe documents using a reference frame to guide the fill. Save the project and keep its generated image sequence assets together.
Return to Premiere and verify the edit
Allow the linked composition to update, then check the complete shot, transitions and audio. Complex compositions can preview slowly. If linking is impractical, render a compatible intermediate for import and compare its timing. Do not judge a moving repair from a single still frame.