Reversible image data hiding (RIDH) is a special class of data hiding techniques, where the host image can be perfectly reconstructed upon data extraction. Due to this reversibility property, RIDH has been widely adopted in many critical scenarios. However, almost all the existing methods focus on improving the capacity-distortion performance; and the hiding ability is ambiguously referred as the perceptual unawareness of a human observer. In this work, we show that the prevalent RIDH framework, prediction error expansion histogram shifting (PEE-HS), would leave quite obvious traces after embedding, suffering the risks to expose the data hiding action. To address this issue, several countermeasures are proposed to conceal the embedding traces while retaining the conventional reversibility feature. The experimental results demonstrate the effectiveness of our proposed method. We believe this work could shed light on the security aspect of RIDH. The source code is publicly available at https://github.com/nbudongli/hideridh.