You can do it here, right now — you do not need the app installed. Enter the email address and password for the account and it is deleted immediately.
This cannot be undone. There is no restore, no grace period and no way for us to put it back.
Erased immediately: your email address, your display name, your password and every sign-in credential, and every session — you are signed out everywhere.
Kept, and no longer linked to you: the expenses and settlements in groups you shared with other people. Your seat in those groups becomes a nameless placeholder.
That is deliberate, and it is worth being plain about: erasing them would silently change what everyone else in those groups owes each other. Your departure must not rewrite somebody else's ledger. The full account is in the Privacy Policy, §7.
Reset it first — the app's sign-in screen has Forgot your password?, which emails a code to a confirmed address. If the address on the account was never confirmed, or you can no longer read it, email owemeapp@gmail.com from any address you can prove is connected to the account and a person will handle it.
Deleting is not the only option. The app can hand you everything the service holds about you — Profile → Account → Export my data — as JSON, and any group as CSV. Do that before deleting if you want a copy: afterwards there is nothing left to export.