One of the most recommended spell checkers for TX Text Control ActiveX is WSpell from Wintertree Software. Recently, they published a solution for the background-checking features with TX Text Control ActiveX 12.0. The background-checking enables developers to display a red zig-zag line as the user types under the misspelled word.
It is neccessary to create a registry key in the WSpell registry path. The complete description can be found here:
Additionally, this site contains sample code that describes how to use WSpell with TX Text Control ActiveX.