How do I remove the Pursuer's curse?

Solution 1:

The effect of curse in Dark Souls 2 is similar to the effect that you get when you die -- you lose some of your maximum health and you go hollow. You can reverse this effect by either using a human effigy or completing a session with the white soapstone (either small or regular).

The curse effect from Dark Souls 1 has been moved to the "petrification" status.

Solution 2:

First of all, in DS2 you don't have to be afraid of curse like you were in DS1.

Curse has the same consequences as death, except for not actually dying:

1. You max hp will be lowered by 5%.
2. If you are human you will become hollow.
3. Once your maximum hp has been reduced to half curse does nothing to you.
4. You can revert curse effects by: using human effigy, using white soap stone and successfully helping other player, or praying at Altar of Amana.
5. In the late game a character can get 100% immunity to curse.

Note that since your character doesn't die you can be cursed multiple times in one fight, losing up to 50% of your hp bar.

DS2's analogue to the DS1 curse effect is petrification, but petrification is still far milder than DS1's curse: you die and lose 20% of your hp, which can be restored with a human effigy.

P.S. Note that in the specific case of the Pursuer that an attack (if successful) will not only curse you, but buff the boss, which is much more important.