Hrqls:
a draw cannot be claimed on this site, it can only be offered.
you have to agree on the draw to be performed

just decline the draw and continue the game while having a cheerful chat about the rules of a draw?

Actually not correct. Where normal rules of chess apply the game is draw when there is a three fold repetition of a position and a player claims it. The issue is that Brainking does not automatically recognise it (it would be very complex to programme I imagine) but the rules on the site advise you can appeal for arbitration. Ideally of course this is settled between the players.