See if you can use a small trowel, or even a sturdy spoon, to get a bit of the soil out of the pot. Then you'll be able to feel its texture, see how it absorbs moisture, see how friable (soft and crumbly) it becomes when wetted. You should also be able to visually observe the larger bits of organic matter.
If the soil gets sticky when wet, rather than soft and crumbly, and if you don't see any evidence of pieces of organic material, in which case it would look more like a homogenous mix, with particles all one size, then I would repot the palms.
When you repot, don't remove the soil that's already there, even though it may not be what the palms prefer. It's more important not to disturb the roots any more than is necessary to get the job done. Gently rough up the outside of the root ball, before you replant in the new soil. (I use an old dinner fork for this purpose, just dragging the tines from the top to the bottom of the root ball, making little shallow furrows in the dirt. You may pull a few root tips loose, but that's okay. If the palms are large, you can use a sharp blade, something like a box knife, to cut little vertical grooves all around outside of the root ball. This will help the roots to grow into the new soil that you provide.)
You may want to have some new containers ready. I would select containers that are one size larger than the pots the palms are in now. Be sure the containers have plenty of drainage holes in the bottom.
If the roots are not tight in the pots the plants are in now, you can crumble away some of the soil around the outside of the root ball. Take off about an inch of soil, if it's possible to do so without digging into the root system itself. That way, you can put them back in their present containers and have room to add new soil around the outside. If you remove some of the soil in this way, then you can skip the step of roughing up the outside of the root ball.
If the roots are tight in the pots the plants are in, then they'll need to be moved to the new, larger containers. In this case, it is
important to rough up the outside of the root ball.
Does all that make sense?
"Isn't it enough to see that a garden is beautiful without having to believe that there are fairies at the bottom of it too?" - Douglas Adams