Context: Th 28 is a Classical T Tauri star in the Lupus 3 cloud which drives an extended bipolar jet. Previous studies of the inner jet identified signatures of rotation around the outflow axis, a key result for theories of jet launching. Thus this is an important source in which to investigate the poorly understood jet launching mechanism. We investigate the morphology and kinematics of the Th 28 micro-jets with the aim of characterizing their structure and outflow activity, using optical integral-field spectroscopy observations obtained with VLT/MUSE. We use spectro-imaging and position-velocity maps to investigate the kinematic and morphological features of the jet, and obtain a catalogue of emission lines in which the jet is visible. A Lucy-Richardson deconvolution procedure is used to differentiate the structure of the inner micro-jet region. Spatial profiles extracted perpendicular to the jet axis are fitted to investigate the jet width, opening angle and the evolution of the jet axis. We confirm the previously identified knot HHW$_{2}$ within the red-shifted jet and identify three additional knots in each lobe for the first time. We also find [O III]$lambda$5007 emission from the blue-shifted micro-jet including the knot closest to the star. Proper motions for the innermost knots on each side are estimated and we show that new knots are ejected on an approximate timescale of 10-15 years. The jet axis centroids show a point-symmetric wiggle within the inner portion of both micro-jets indicating precession. We use the jet shape to measure a precession period of 8 years, with a half-opening angle < 0.6$^{circ}$. This may provide an alternative explanation for the rotation signatures previously reported. We find the jet shape to be compatible with precession due to a brown dwarf companion orbiting at a separation $leq$ 0.3 au.
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