what=the thing(s) which 为特指概念。

whatever= anything that 为泛指概念，用于非肯定语境。

本句中主句谓语为一般过去时，表示确实发生的事件，为肯定语境，故不能用anything that.

例如，我们可以说I took everything in the bag. 但不能说 I took anything in the bag. 可以说 I saw someone in the room. 不能说 I saw anyone in the room.

因此，本句应选what, 而不是whatever。

如果主句谓语改为 I would take, 则what 和 whatever 均可以。因为，我们既可以说 I would take the thing that was left in the bag. 也可以说 I would take anything that was left in the bag. 情态动词would的使用，表示主句的动作 take 还没有发生，袋子里是否有东西可能是提前知道的，也可能提前无法知道，故what 和 whatever 都可以使用，但意义有差别。