Confirm which storage limit was reached
Check the mailbox's reported usage and the account-level object storage available to it. Mail content and attachments can contribute to stored data, and removing messages may not immediately change the displayed usage if cleanup is still in progress. Use the mailbox's own usage view where available rather than estimating from message count.
A rejection at receipt means the sender may need to resend after space is available; the message should not be assumed to be waiting safely in the recipient's inbox. If the sender received a delivery failure, keep its timestamp and reason so you can confirm whether it was a quota rejection.
Free space and prevent repeat failures
Remove or archive messages that are no longer needed, especially large attachments, following the product's retention controls. Then recheck usage and make sure enough account storage remains for new mail. If the account is shared across services, consider how other stored files affect the same allowance.
After space is available, ask the sender to send a new copy or use the normal resend flow. Send a small external test message and confirm receipt before relying on the mailbox again. If usage appears below the limit but messages are still rejected, capture the sanitized error and contact support with the mailbox identifier.