Mobile robots will play a crucial role in the transition towards sustainable agriculture. To autonomously and effectively monitor the state of plants, robots ought to be equipped with visual perception capabilities that are robust to the rapid changes that characterise agricultural settings. In this paper, we focus on the challenging task of segmenting grape bunches from images collected by mobile robots in vineyards. In this context, we present the first study that applies surgical fine-tuning to instance segmentation tasks. We show how selectively tuning only specific model layers can support the adaptation of pre-trained Deep Learning models to newly-collected grape images that introduce visual domain shifts, while also substantially reducing the number of tuned parameters.