No, Boxing Day is not a day for returning unwanted Christmas gifts. Boxing Day is traditionally celebrated in Great Britain on December 26th, a day when civil servants and tradesmen would receive gifts from their superiors.
This custom is linked to an older English tradition since they would have to wait on their masters on Christmas Day, the servants of the wealthy were allowed the next day to visit their families. (Downton Abbey-esque)
The employer would give each servant a box to take home containing gifts and bonuses, and sometimes leftover food. In general term, it’s a gift sharing day.