The arms are probably based on the arms of the Alsager family (listed in reference sources under Tryon). The Alsager family were settled in Cheshire by the 13th century. By marriage the name Tryon became associated with the Alsager name in 1819.
To this has been added a chevron showing three wheat sheaves for Cheshire.
The arms on a mug (1919, image from eBay)
Literature : Image from Facebook