Caffeine and Theophylline are both methyl xanthines which seem to have similar physiological effects on the cellular level. Can you remove one from a food without removing the other?
Supercritical fluid extraction (SFE) method may be useful to obtain decaffeinated black tea. But SFE technique not only reduced caffeine but also reduced theaflavins, thearubigins, colour and brightness which are some important features of black tea.
I suggest to read article Joshi, et al., (2013). Effect of decaffeination conditions on quality parameters of Kangra orthodox black tea, published in Food Research International. doi: 10.1016/j.foodres.2012.12.050