When the speed of a particle increases, its rest mass

The rest mass of a particle is an intrinsic property and is independent of its speed or the frame of reference.

While the relativistic mass of a particle increases with speed according to the relation $m = \dfrac{m_0}{\sqrt{1 - \dfrac{v^2}{c^2}}}$, its rest mass $m_0$ remains constant.

Therefore, when the speed of a particle increases, its rest mass remains the same.