The edge-cloud continuum is an advanced paradigm for cloud computing, which brings data storage and compute power closer to users or devices, and as a result, eliminates lag time and saves bandwidth. However, this new paradigm is harsh for secure storage and computation due to the separation of data ownership and control. Data security, especially outsourced data integrity in the edge-cloud resilient network, becomes one of the most fundamental challenges. To check the outsourced data integrity and address the efficient key update issue in this scenario, in this article, we propose a framework of outsourced data integrity checking with a practical key update in the edge-cloud resilient network. We first review the existing outsourced data integrity checking algorithms and then put forward a potential solution to achieving outsourced data integrity checking with a practical key update, which is composed of three phases, namely key request and update, local data upload, and outsourced data integrity auditing. We implement a prototype system for our proposal as well, which demonstrates its practicality.