IANAL but this doesn’t sound so bad actually. If you simplify the language and distill it down, it sounds to me like that are basically saying they may share your info with other parts of themselves (any other [entity] that controls, is controlled by, or is under common control with, DeleteMe).
This doesn’t seem to grant them permission to share any data with actual 3rd parties (but of course they must, the entire purpose of the service is to interact with 3rd parties on your behalf, and in the context of opting out from data brokers, they must often provide personal information to confirm your identity to complete the opt-out, so I imagine elsewhere in the privacy policy this will be outlined somewhere).