Have you tried with different PatternWidth, PatternSkipWidth etc, also backgroundsprite's tile width has effect.

So if main image has 1 pixel wide bordering on tiles (black lines), and each tile is 31x31, then these settings would do:
PatternWidth: 31
PatternSkipWidth: 1
TileWidth: 31

Haven't used DelphiX for long time so unsure what exactly the variables are called... But it could also be small bug in unDelphiX where you would need to try 1 pixel larger approach to fill the gaps.