Extraction of a multiple [t,f] area from Continuous Wavelet Transform

I am trying to de-noise a transient signal, which contains noise superimposed to a quasi-step variation at a certain point in time.

If I calculate a CWT, of course I have a significant area in which the coefficients are high at the time of the step change plus some noise at high frequency mainly.

I think that a first idea to de-noise the signal would be to extract time frequency area from the CWT scalogram, I would say a reversed T area in the map, the sum of two [t1 -t2 ,f1 f2] rectangles. Is it possible to to do this using the cwt and icwt data? It seems that it is just possible to extract a frequency band, i.e. a [f1 f2] rectangle using icwt.

If this is possible and makes sense, is this concept extendable with the use of the Discrete Wavelet Tranform.

Thanks for your suggestions and help.

E.