Unfortunately there is no undo button available in every game.

There should be. Why isn't there? Bad programming.

 A 'take back' button would be nice option but it can also be used for some abusive players, offering undos is basically giving a tool for people to be annoying and rude when they are about to lose the game.

In real backgammon, an undo is allowed on the first of the two checkers being moved. Programming should allow for this and would be easy to program.

In real backgammon, in Greece, 'the table catches' - meaning your moves are unchangeable - good thing or bad I don't know, but basic rules.

uh, i don't live in greece.  there are a lot of good points here
i spent a long time looking for a way to figure out how to undo my move, not realizing the games were timed
do they have time limits in greece as well
here's the point: why don't you make taking moves back optional, by placing a check box in the game, or making it an option in the settings
this way, if you live in greece, you can still play tables that "catch"