You are able to use the Aircall Dashboard to check and delete call recordings and voicemails as detailed here.
Currently it is only possible to delete entire recordings, and it is not possible to delete only parts of a specific recording or voicemail. If a user forgets to pause the call recording when taking sensitive information over a call, and the recording needs to be deleted, you will need to delete the entire recording as deleting only that specific part is not possible at the moment.