In the council of Elrond it is debated whether or not to send the ring across the ocean and transport it to Valinor. That idea is however quickly rejected as it is mentioned that they would not receive it, as the Ring was part of middleearth and thus for the races that dwelled there to take care of.
But what about the Balrog/Balrogs? Where the Valar aware of them? If they weren´t but was made aware, would they once again have traveled to Middle Earth to remove them? Or do they consider the problem of the surviving Balrogs, to be in the same league as that Ring and Sauron. Something that the men, elves and Dwarfs of Middle Earth must take care of themselves, as the Valar will not interfere directly in the affairs of Middle Earth again?