Eddie alerts to blood and cadaver scent. Keela didn't alert which means Eddie's alert couldn't have been to blood. Cadaver scent is made up of many volatile compounds including cadaverine. Pus contains no cadaverine.
Eddie also alerts to blood, according to Grime.
I don't find it clear what exactly Grime means by "cadaver scent". Some dogs have been known to falsely alert when searchng for bodies in peat bogs - because they give off methane, and that's one of the VOCs. A whole body won't smell the same from one period to another, nor will one type of body part necessarily smell the same as a different one.
And I still don't know what Grime meant by scents he was trained to detect (as opposed to what he would specifically not react to that is also subject to decomposition recognisable by a dog).
What was he reacting to on the sex tissues in Jersey? A speck of blood or semen/vaginal secretions? Or both? Presumably the tissues didn't indicate anything of relevance to the investigation.