Here's my experience. When I deleted my Parler (I barely even used it), I wrote a detailed email asking them to confirm if my residual data was also deleted (email and phone number), because when I did a test run to recreate my account, it said that my email was still in use. I also requested that such information be deleted.

Despite my email being clear, the replies were automated like those automated call options and were not at all related to my request. e.g.:

If you are not sure of your login email, please go through Account Recovery, as that is the only safe route that Parler can provide this. To retrieve this information, please go through Account Recovery on the login page. From there, we can walk you through the steps! At this time, Parler cannot disclose emails.

Finally after I dropped the polite tone and gave them a one-liner, a real human came back and just said, "Oh I can confirm it's deleted." When I pressed them for details, they replied with this:

Hello!

Even if an account is deleted, the email address and phone number used stays linked to ensure multiple accounts are not created with the same information.

Parler Support

And the request for that information to be purged from their servers? Unanswered.

This email string continued over 3 months. So after being stonewalled by an automated system and by an unhelpful support team, all I got was, "You're deleted but your email and phone are actually retained just in case someone decides to impersonate you."

I didn't raise hell about this since I didn't foresee Parler getting taken out like this, but, well, here we are. I did post here about them maintaining residual data but Parler was like a free speech oasis.