Retching-under-Tweed was a village in England that, according to legends associated with Saint Fidgeta, may have been near a medieval Fidgettine (or either Saxifragian or Ursuline) convent (Saint Fidgeta and Other Parodies; 24).
The River Tweed is 97 miles long and flows primarily through the Scotland/England borders region of Great Britain.
Bellairs appears to be having some fun with the naming conventions of villages and towns along rivers (e.g. Stratford-upon-Avon indicates the village of Stratford was built upon the River Avon). So does that mean this village was named after someone was found retching under the River Tweed? Directions to a city or hamlet named Retching are up for grabs. We doubt it has to do anything with undesirable or ugly tweed garments, as tweed is usually outerwear (not "under" wear).