Total guess, no testing has gone into this: -

CREATE FUNCTION [dbo].[fn_QBRemoveNonAlphaChars] (@String VARCHAR(1000))

RETURNS VARCHAR(1000)

AS

BEGIN

WHILE PATINDEX('%[^a-z ''-]%', @String) > 0

SET @String = STUFF(@String, PATINDEX('%[^a-z ''-]%', @String), 1, '')

RETURN @String

END

You had the ^ character in your "allowed" pattern.