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Does renormalization mean discarding corrections to a known constant?

I mean, we assign a known value to the electron mass or charge, whatever, in the zeroth order of the perturbation theory, for example, in QED. In the next order we obtain a correction to this value (finite, for instance). AFAIK, the renormalization means replacing the known constant+correction by the same known constant. To justify this, one says that the constant is not known anymore but "bare" now and only the sum is observable.

In my opinion, this replacing may be understood without ambiguity as discarding the correction and keeping the known value intact. Is it so?

Thanks,

Bob.