I Don‘t think there is a way to do that without disassembling it which I would not do for safety reasons (also it is probably a small neon lamp and not a LED).
The way I usually do it is either with a black marker (just draw over it), some black duct tape or a combination of both.
The description does not mention an on/off button, but something else "With reset fuse button".
This is a fuse built into the power strip to prevent it from being overloaded. That is why the black ring around the red button should also say "Press to Reset", so that the fuse can be reset if it has tripped.
Is either a fuse or an on/off button. However, the picture is probably wrong because the Brennenstuhl website shows the product (same item number) without a button.
I ordered the power strip for someone else. Unfortunately, I no longer have it at home. But it must have been between 40 and 45 cm long and about 4-5 cm high, just like the others. Unfortunately, I can't give more precise information.