Alrighty, progress but not quite there yet. I read in a couple of different places that I should try to set up Object Mapping, mapping to the class of the grid. I did that and am now receiving an errors which states "Invalid number of parameters".
As I remember TwwDBGrid (woll2woll) does not expose it's data or data source. I mean that you cannot access to grid's data thus you cannot create any checkpoint for it. I don't think that setting any object mapping helps.
If it's possible ask your developers to use TDBGrid, which is supported by TestComplete and should works fine.
Or maybe Smartbear can do something with support to this control ?