Problem with a solar power bank indicator LEDs
Most LEDs have a nominal current of 20mA. By choosing a larger resistor, the current can be reduced, but their light becomes dimmer. 
There are LEDs for just 2mA, saving 90% of current / energy without being too dim. 
So, changing the LEDs may also be an option, if the device doesn't already use low-currrent LEDs. 

However, what's the size of your solar panel?  If it's 10cm x 10cm = 0.1m x 0.1m = 0.01 square meters, it catches only 10W of sunlight.  (The sun gives us a maximum of 1kW per square meter) 
The efficiency is as low as 20%, resulting in just 2W electrical power gained. At 5V, that's just 400mA.

So, one to three 20mA LEDs are noticeable consumers, but 2mA LEDs are not. 

Now you say your powerbank holds a charge of 4000-10000mAh. It takes 10-25 hours of bright sunlight to collect this charge. 

In reality, there are power conversion losses and sunlight isn't always as intense as in the Sahara at 12 o'clock. You can for sure add 20% to the charging time, maybe more. 

So, don't expect too much from the solar module.