LTC3106 solar harvester example allows current flow into the solar cells
Yes, the highlighted capacitors will discharge through the solar cell.

This will not harm the cell; for each event of darkening and assuming nothing else is discharging the capacitor, you'll just get that

$$\tfrac{1}{2}(110\,\mathrm{\mu F})(4.9\,\mathrm{V})^2 = 1.3\,\mathrm{mJ}$$

of energy dissipated in the cell (by way of the forward voltage drop of the solar cell considered as a diode), which is far less significant than the heating it will ordinarily experience by being exposed to sunlight.



If the solar panel were instead connected in parallel with your primary energy storage (say a battery or supercapacitor), this configuration would be unwise since the dark panel would in fact fully discharge it (whether or not the panel is also damaged by that current).

In that situation, a diode (or a FET switched by a controller, to avoid the voltage drop) should be placed in series with the solar panel to avoid the reverse current and discharging.

But this is not that situation, and your LTC3106 chip will presumably be doing the right thing with its two power inputs.