Viscocity and exchange of material between different mediums In the book of S. Vogel, Life in Moving Fluids, at page 29, it is stated that

Lower viscosity at higher temperature implies steeper velocity
gradients and thus thinner gradient regions on surfaces. In effect, a
solid surface is less shielded from free stream flow. That ought to
help the exchange of dissolved material between an organism and moving
water around it.

how is the steeper velocity gradient supposed to help the exchange of material between two different medium, namely an organism and the fluid around it.
 A: A common boundary condition in fluid-solid interaction is the assumption that the fluid exactly at the surface of the solid has the same velocity as the surface. These are so-called no-slip boundary conditions. Viscosity (roughly) tells you how much neighboring fluid elements can differ in velocity, low viscosity allowing for high differences. So at low viscosities, the flow is only stationary with respect to the solid boundary in a very small layer above the boundary. This means, as Gert's answer points out, that you get more turbulence. Turbulence starts brushing fluid back and forth on your surface, chipping away bits of the surface and leading to a higher exchange of mass.
You can easily check for this effect at home. Let some dirt dry to a teaspoon (mud should do fine). If you wiggle it around in water, you wil get rid of it. Try repeating the same process with honey. No chance of getting that spoon clean.
You may also find the wiki article on boundary layers interesting, https://en.wikipedia.org/wiki/Boundary_layer. Don't get too absorbed in the math. There's even a section on heat and mass transfer, though you need to know about the Prandtl number to follow, which is viscosity over thermal diffusivity (Ludwig Prandtl spearheaded the analysis of boundary layers in the early 20th century).
A: 
how is the steeper velocity gradient supposed to help the exchange of
material between two different medium, namely an organism and the
fluid around it.

Steeper velocity gradients means higher turbulence, which in turn means higher material transport through convection. Mass transport is very similar to heat convection in that respect: turbulence favours the carrying off of material from a surface to a fluid.
Turbulence is of course favoured by low viscosity (see Reynolds number $\text{Re}$)
