Clinical examination of chronic pressure wounds involves partial tissue segmentation, an important diagnostic component. However, the entire automated process can be complex due to the different tissue types, which are visually close together. In this paper, a model of interactive segmentation is presented that incorporates user-manipulable point prompts directly into the DeepLabV3+ model. This 4-channel representation was developed by adding a localized Gaussian heatmap to the standard 3-channel RGB input, computed from points sampled from the largest connected component of the target tissue, providing the model with the required spatial priors. The model was tested on a clinical dataset using 5-fold patient-aware cross-validation. Comparisons with data augmentation techniques were also analyzed. The 4-channel model configuration that achieved the highest performance produced a Dice Similarity Coefficient (DSC) of 0.958 for the holistic wound bed. Furthermore, when data augmentation was applied, the interactive model yielded big differences and steady improvements across single-tissue-trained models. The results suggest that a simple human click substantially helps to achieve successful segmentations of the variety of textures present in clinical wound management.