Bonksquad is a fan-made raid planner for World of Warcraft guilds. It isn't made by Blizzard or Discord.
What it keeps. When you sign in with Discord: your Discord user ID, display name and avatar, and which of your Discord servers are linked to a guild here (to let you join that guild). Your guild keeps your characters, sign-ups, loot and points, and a log of changes. Characters you save on your account page are kept with your account.
What it doesn't keep. Your email, your messages, or your Discord password. Bonksquad never reads chat.
Cookies. One sign-in cookie, and a short-lived one while you sign in with Discord. No tracking or adverts.
Deleting. On the Your account page (in the account menu), Delete your account removes the account and your Discord details. Your characters stay on the guild roster with no owner, because the guild's history uses them.
Questions. Ask the person who runs this site, or use Suggest a feature in the account menu.