That's a unicorn you're showing to the right of the armorial in the picture. There is a lion (not shown) on the left hand side and these are the two supporters for our royal coat of arms. The arms on your pipe are in the style used between 1714-1800
As you probably know, the 33rd arrived in America in 1776 and fought in the War of Independence until captured in Yorktown in 1781 and interred until the end of the conflict. One detachment was in Charleston at the time and escaped capture by withdrawing to Canada in 1782.