Recliner chair back sections normally have metal sliders which slide down onto two metal spikes on the recliner action. There is generally a locking clip at the top of each slider which latches into a hole in the spike. I would free the spike and slider that are still in position by pulling the clip and simultaneously pulling upwards on the back panel. This should remove the entire back section. You can then locate both spikes into both sliders and push down on the back section until they click locked.
Richard Oldroyd, October 2014