本句变成间接引语时态可以不变：

He said that he was glad that he had caught the early bus.

参考例句：

He said that he was sure he had left it in the room. 他说他肯定把它忘在房间里了。(英语语法教程)

She said that she was deeply moved by all the letters of sympathy she had received. 她说她为收到的所有慰问信所深深打动。(剑桥高阶词典)