The Unexpected Finger propelled herself by burning iron into photons, which flew out her exhaust pipe.
How much iron?
As Sir Newton captured so beautifully in his famous Third Sonnet, parting is such sweet conservation of momentum. Which means the Finger's momentum changed by an amount equal to the momentum of her departing exhaust, but in the opposite direction.
The momentum of an exhaust photon is given by
Oh screw that. The finger is just an ideal photon rocket. Her mathematics were worked out in the 1950's. Her maximum velocity is v = c (Mi2‑Mf2) / (Mi2+Mf2) where c is the speed of light, and Mi, Mf are the ship’s initial and final mass. (Fuel consumed = Mi ‑ Mf.)
This equation even accounts for all that wacky Einstein stuff, which is minor at 0.2c.
Let's plug in some real numbers. And when I say real, I mean fictional, even though Gaia's Wasp was based on actual historical events that could have happened.
I'll compute the Finger's fuel consumption by trial and error. That is, I'll take a guess at the Finger's fuel consumption, then compute her velocity with the ideal-photon-rocket formula, then adjust my guess and try again. For a first guess, let's say her fuel consumption was 730 tons. Since her initial mass was 4000 metric tons, her final (arrival) mass would be 4000‑730=3270 tons. Plugging those numbers into the formula gives the Finger's velocity v = c (Mi2‑Mf2) / (Mi2+Mf2) = c(40002‑32702) / (40002+32702) = c(5307100 / 26692900) = 0.2c.
Wow, v = 0.2c, just like in the book. I got her fuel consumption right on my first guess. What are the odds?
So to decelerate from 20% of the speed of light, the Finger had to burn 730/4000  = 18% of her initial mass, which was 22% of her final mass, or a non-coincidental 20% of her average mass.
How was her mileage? The Finger decelerated for a period of 210 days, which is 1.8×107 seconds. Thus her burn rate was fuel / time = (7.3×105kg) / (1.8×107s), or 0.04 kg/s. In commoner units, the Finger's fuel consumption was 1.4 ounces per second.
Wait, 1.4 ounces of mass converts into almost a megaton of energy. The finger decelerated by firing a megaton per second out her tailpipe?
A megaton per second raises a question, which I will try to phrase delicately:
Did the deceleration squish the crew?