Perhaps Mohammed is referring to the longevity of ink vs. blood.
The scholar's ink, I believe, is reference to writing, particularly history, events, etc. Writing is a way of recording these things almost permanently.
One really good example of this is a line from the movie A Knights Tale. Chaucer (a writer) tells his enemies, “I will eviscerate you in fiction. Every pimple, every character flaw. I was naked for a day; you will be naked for eternity."
Although martyrdom is a sacred act, it is not a permanent memory. Once the act is done, unless it is recorded, either by writing it (more likely!) or by word of mouth telling (not always as reliable/ long lasting as writing) it will most likely be forgotten.