No, but you can talk about changes in perturbations of fields over time in QFT (which has its own representational issues). A particle is a useful metaphor.
Their point in this case is that a wavefunction is spread out over space, which would cause it to be subject to a local clock gradient in curved spacetime. If you wanted to use particles, you'd need to use a Feynman-style "integrate over all possibilities" approach, which would again be subject to a clock rate gradient over space.
The mathematics of this is a bit too complex to reproduce in a comment here, but in, say, the Earth's gravitational field, taking this effect into account (approximating GR as a field of locally varying clocks, then allowing, e.g., an electron's wavefunction to evolve on that spacetime) would reproduce gravitational acceleration / free fall towards the Earth.
Said differently: this is precisely the kind of nuanced scenario where getting sloppy with metaphors gets you into trouble very quickly. Quantum mechanics in curved spacetime is not to be dabbled with lightly.
I think it takes a very narrow understanding of physics discourse to call the particle a terrible metaphor. What's next, entirely discarding the teaching of newtonian physics in high school?