Podficcers! Here are some sample permission requests for you to use and tweak as needed.

If the author has no permission statement:
Hello! I'm [name] and I made a podfic of your fic [fic title]. I'm joining a fic challenge to have a remix written of one of my podfic, and I'd really love to submit this one (you can take a look at the challenge here: remixapod.dreamwidth.org). Would that be ok? Please let me know either way! [Your name and sign-off]

If the author has a permission statement, but it doesn't cover remixes:
Hello! I'm [name] and I made a podfic of your fic [fic title]. I'm joining a fic challenge to have a remix written of one of my podfic, and I'd really love to submit this one (you can take a look at the challenge here: remixapod.dreamwidth.org). Your permission statement doesn't cover this, so I thought I'd check in with you about it. Would that be ok? Please let me know either way! If you are cool with remixes of your fic, please consider adding that to your permission statement! [Your name and sign-off]

(If you use/have used a different permission request, please feel free to add it in the comments! I know my particular personal style will not be for everyone :D)