Pensieve header: Tbar games - $\bar{T}=(T-1)/h$.

Series[(1-(T^2)(E^(-2ϵ a ℏ)))/ℏ, {a,0,3}]

Simplify[(1-(T^2)(E^(-2ϵ a ℏ)))/ℏ /. T ->1+ℏ (OverBar[T])]

Simplify[((1-(T^2))/ℏ) /. T ->1+ℏ (OverBar[T])]

Simplify[Series[(1-(T^2)(E^(-2ϵ a ℏ)))/ℏ, {a,0,3}] /. T ->1+ℏ (OverBar[T])]

Simplify[((T-1)/ℏ) /. T->(T^(-1)) /. T ->1+ℏ (OverBar[T])]