Microwaving dyes and synthetic fabrics doesn’t seem safe
Microwaves are tuned to heat water molecules.
They’ll pass right through fabric and plastic/synthetics.
The standard technique to heat non-water based things is by using a thin layer of foil (e.g. microwave Popcorn or some instant meals).
It could be a gel too, but there may be a danger if hot leak.
Unless the plushie is on fire when it’s given back to the child, I don’t see how this could go wrong.
Heating plastics can release VOC. Many plastics will get hot in a microwave. It’s recommended not to heat food in plastic containers for this reason
This applies to food, I doubt it’s relevant in this scenario, but I am open to being proven wrong.