What are the most suitable methods for correcting sudden DC offsets or baseline offset? and Why? See the image for the use-case or example
I'd do this nonlinearily, in two steps:

Detect the jump
Correct the jump

Detection sounds rather easy: a short (linear-phase) high-pass filtered version of your signal is compared to a threshold. From that, we know exactly the position of your jump; it's where the threshold was crossed, minus the group delay of the filter (which happens to be half the filter length).
Take the value of the original signal right after the jump. Shift the right-hand side of the original signal such that it ends up at the same amplitude as the sample before the jump. (A more elegant way would be definining a signal model, and then modeling the most likely signal progression, but you don't seem to have an overly useful signal, as you don't mention it.)