For reference, here's the Firefox logo:
Even stricter scholars don't include "incomplete images" as haram, e.g., Islam Q&A wrote:
It seems that images which do not have complete features, which do not have a nose or eyes, are not included under the heading of haraam images, and the ones who make them are not included in this warning, because they cannot truly be said to be images, and these images do not imply imitating the creation of Allaah.
In fact, IslamWeb was indeed asked about the Firefox logo (among other logos). Relevant here is:
Firstly, if the image of a face is without a body, it is not included under the prohibited images. Ibn Qudaamah may Allaah have mercy upon him wrote, "The same applies to incomplete images, such as the image of a body without a head, or a head without a body, or an animal's head attached to the body of a non-animal; this is not included in the prohibited images because it is not the image of an animal." [Al-Mughni]
Secondly, there is no harm with the images of animals that are defaced in such manner that their features are unclear. This applies to the bird in the Twitter logo. Ibn Nujaym may Allaah have mercy upon him said, "...likewise, if the image is defaced, it is the same as the image without a head." [Al-Bahr Ar-Raa'iq]