It looks as though TG made a schedule change - cancelling flights on Tuesday and Thursday - after you made your booking. 9.1.2 of their Conditions of Carriage give them the right to make changes and offer you alternatives.
If you are booked on a discounted TG Business Class ticket this will only be valid on TG services. If they rebook you on another airlines service they will have to pay that airline the full cost of the ticket; something they are highly unlikely to do. Airlines will do this on the day of departure if a problem arises that means they cannot operate the service but this far from the date of departure they will reschedule.
I think you will spend a lot of time and energy on this but end up with the same result - the offer of a refund or transfer to other TG operated flights on a different day.