Grid cells of the medial entorhinal cortex (MEC) have been proposed to play a key role in navigation. Competing models suggest they contribute to spatial localisation in general or have a dedicated role in path integration. Here, we aim to distinguish these possibilities by investigating how grid and non-grid cell firing varies as a function of performance in a virtual reality location memory task that can be solved either with a cued-based strategy or exclusively by path integration. We take advantage of spontaneous variation within and between recording sessions, which gives a complementary approach to perturbation-based studies by correlating grid activity with task success without confounds from circuit manipulations. We recorded neural activity in the MEC of mice exploring an open arena followed by a location memory task (https://doi.org/10.1016/j.celrep.2018.01.005). We found grid firing patterns could either be anchored to or independent-from the task reference frame. Task anchoring varied across and within sessions, with non-grid cells either following the grid anchoring mode or remaining stably anchored to the track. When the reward location was marked by a visual cue, making the task solvable via a cue-based strategy, performance was similar whether grid cells anchored to the track or not. On the other hand, when no visual cue marked the reward location, making path integration the most efficient solution, performance was enhanced when grid cells anchored to the track. Our result suggests anchoring of grid fields is important for accurate path integration, consistent with location estimation models that utilise anchored grid codes.