The "stuff" is coming from the joints of the legs, where the leg meets the abdomen. Yes, this is the one who had trouble molting. She is showing no interest in food and has not ate since her molt. I rubbed cricket guts on her raptors to try and get a feeding response but no luck.
If it's not continuing to flow, it looks to me like hemolymph which has scabbed, it tends to darken considerably. It's coming from the joint of the trochanter and coxa correct? It's probably a wound she sustained during the strained molt. She may be alright, I have had some adult mantids with pretty profound injuries who have lived normal lives (one was hit with a weed-eater). Make sure she's well-hydrated and try feeding her again later today or tomorrow.
So yesterday I held my ghost mantis and tried to get her to eat. She took a few bites from a dead cricket for 30 seconds and then refused to have any more. It's hard to get her to eat at this point. Her back is also curved in so she cant stand up straight.
Is she scared of the stick/spoon/syringe? My P.paradoxa is easily scared. I fed her honey once, but i had to be really patient and persistent to get her to eat it.
Can she bring her raptors to her mouth? If yes, you could try and put some on her raptors. She'll clean them and and get the nutrients that way.
She is not able to hunt food herself?