The most efficient way to purify CNTs from amorphous carbon is heating at 400°C for several hours under ambient atmosphere to burn it.

Of some possible interest concerning to you query: https://www.researchgate.net/post/how_can_I_dissolve_the_coconut_shell_charcoal https://www.researchgate.net/post/Is_there_a_solvent_that_can_dissolve_amorphous_carbon

I would say that the real problem here is NOT how to dissolve amorphous carbon, but how then to SEPARATE purified MWNTs from the huge amount of solvent and dispersant. It is much more practical and ecologically friendly not to use liquid phase AT ALL.