In imaging geometries, which employ wavefront-shaping to control the light transport through a multi-mode optical fibre (MMF), this terminal hair-thin optical component acts as a minimally invasive objective lens, enabling high resolution laser-scanning fluorescence microscopy inside living tissues at depths hardly accessible by any other light-based technique. Even in the most advanced systems, the diffraction-limited foci scanning the object across the focal plane are contaminated by a stray optical signal carrying typically few tens of % of the total optical power. The stray illumination takes the shape of a randomised but reproducible speckle, and is unique for each position of the focus. We experimentally demonstrate that the performance of imaging a fluorescent object can be significantly improved, when resulting images are computationally post-processed, utilising records of intensities of all speckle-contaminated foci used in the imaging procedure. We present two algorithms based on a regularised iterative inversion and regularised direct pseudo-inversion respectively which lead to enhancement of the image contrast and resolution.