I think TTP itself did it but the fear of losing public support is the reason they cannot openly admit it. We all know that if not all but major public of Pakistan and Peshawar in particular are sympathetic towards taliban so this can be one reason. Also, It might be possible that they sent the bombers to target some military installation and/or some other Gov organization and/or people but due to a failure in plan or some miscalculation caused the bomb(s) to be exploded (I am trying to say, maybe TTP was really not wanting to target the public and wanted to target an official installation or army or something but things went wrong and now to avoid hatred from the public they are refusing to accept responsibility) but the style was typical TTP style so I will be surprised If TTP was really not behind this

Also, Why should we listen to TTP and consider their word the final one and/or consider it to be true? They too can lie and so can anyone else, so just because they claimed they have not done it we should not eliminate the possibility of their involvement

BTW, 34 people were killed or 39? You mentioned 2 different figures.