The idea that the velocity comes from one of a binary pair going supernova and the other being flung off after the mass of the supernova star is removed is the standard proposal.
However, let's look at my alternative proposal in a couple of ways, both where the star does *not* absorb the mass of the impacting planet.
First, let's say the mass of the planet, at that very high speed, is not stopped but passes right though the star. As you say initially the star is moving toward the planet while the planet moves to the star. To make up that high momentum of that many Jovian mass planet, the star would be made to move at a velocity some fraction of the thousands of km/sec velocity of the planet. At thousands of km/sec for the planet and if several of the high Jovian mass planets impact the speed of the star could be up to 100 km/sec.
After awhile they both or all would be made to slow down and come back together. But if the planet(s) took millions of years to impact it could take millions of years for them to come back together.
Secondly, suppose they impact in an elastic collision. Then they both would be sent backwards at that very high speed at which they impacted.
Some variations on these are possible. For example, suppose while passing through, the huge mass of the planet tears off a great mass of the star, then while slowed by the impact and by the remaining gravitational mass of the star, this total mass would still be moving at a tremendously high speed. It could be taken for a full star by the extended dimensions of the gas cloud. The original star losing its nuclear furnace might be unrecognizable as previously being a star.
Or as a variation of the second possibility it could be a tremendous amount of material is flung out from the star after the impact and the remaining star would be sent off in the reverse direction from momentum conservation.
Note that in this case there would undoubtedly be caused *very* many thermonuclear explosions or a tremendously massive one due to the high pressures and temperatures produced by the impact which would also cause the star to move in the reverse direction.
Also, instead of an actual planet the impact could be due to a brown dwarf which can have up 90 Jupiter masses, thus imparting higher energy and velocity to the star.

Bob Clark