If the parcel is damaged when it is in the Bringme Box, the general liability rule for any use of Bringme applies. You can find this in the "General Terms & Conditions" under "Profile".
If the parcel is damaged after the Bringme Box is opened by the courier, liability lies with who's responsible for the shipment (as the case may be, Bringme or the courier), and you'll only be entitled to compensation in accordance with the general terms and conditions you agree to when ordering your shipment.
In any case, Bringme will provide support to deal with the damage and compensate you if need be, should you be entitled to compensation.