Numerous methods have been introduced to reliably detect digital face image manipulations in the past. Of late, the generalisability of these schemes has been questioned in particular with respect to image post-processing. Image compression represents a post-processing which is frequently applied in diverse biometric application scenarios. Severe compression might erase digital traces of face image manipulation and hence hamper a reliable detection thereof. In this work, the effects of image compression on the face image manipulation detection are analysed. In particular, a case study on facial retouching detection under the influence of image compression is presented. To this end, ICAO-compliant subsets of two public face databases are used to automatically create a database containing more than 9000 retouched reference images together with unconstrained probe images. Subsequently, reference images are compressed applying JPEG and JPEG 2000 at compression levels recommended for face image storage in electronic travel documents. Novel detection algorithms utilising texture descriptors and deep face representations are proposed and evaluated in a single image and differential scenario. Results obtained from challenging cross-database experiments in which the analysed retouching technique is unknown during training yield interesting findings: (1) most competitive detection performance is achieved for differential scenarios employing deep face representations; (2) image compression severely impacts the performance of face image manipulation detection schemes based on texture descriptors while methods utilising deep face representations are found to be highly robust; (3) in some cases, the application of image compression might as well improve detection performance.