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Okay, I see there have been some interesting messages so far. Let me
indicate two ways of getting the answer I got. Then you can see if
there's a flaw in it.
METHOD #1. Use the result for escape from the solar system and simply
"turn off" the sun's contribution.
For escape from the solar system, the escape speed is given by
Problem 5.17 in Barger and Olsson "Classical Mechanics" (2nd ed.) to
be:
v = (v_earth,esc)^2 + (v_sun,esc - v_earth,orbit)^2 = 16.7 km/s
relative to earth. Here v_sun,esc = 42.1 km/s. Now set v_sun,esc = 0
to get my previously quoted answer.