Any LED has a maximum allowed amount of heating. A small surface-mounted LED cannot dissipate much heat into ambient air so it cannot have much current.
A white LED has a fixed voltage of about 3.3V and if the current is 20mA then it heats with 3.3V x 30mA= =0.1W which is too much for a tiny LED. If the current is 100mA then the heating is 0.33W which will smoke it. The solar panels appear to make 5VDC. Then the rechargeable battery is a little less than 5V. If you apply more voltage then the LED current increases a lot and destroys them.
They can make the light brighter by using more current in the LEDs, then the LEDs, battery and solar panel must be larger or have higher quality.