I know on fleshing a muskrat there is a red, muscular membrane called the "mantle" that is left on the skin. I see a similar thing on my coyotes. I have been told to be careful not to over-scrape coyotes.

Should I leave the "mantle" on a coyote pelt or try to scrape it all down to clean white leather like I do on a coon?

If there is a lot of fat under the saddle,remove it.
If there is a little fat under the saddle,it can be pushed out from under it with a scud (dull flesher).
If there is no fat under the saddle,leave it.

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ but, use care not to over-scrape the pelt and expose the hair roots.

What is " a lot " and what is " a little? " Like is " a lot" like 1/8 inch or more? " A little" 1/8 inch or less? Not for me, I know what to do, but these terms are not very descriptive for the OP.

Good question. All I really know is to get the excess meat, that is not bonded tightly to the hide, and fat off WITHOUT exposing the hair roots.

When the graders get those on the table they do not flow right when they are flipped. So they inspect from the back, some guys just do a peek-a-boo and do up 18 inches and leave the rest. ( they are trying to get out of work). That remaining tissue is an unknown to the buyers when it is dressed and how soon it is done. They do not go into the best piles that is for sure.

For all intents and purposes it is best to leave the saddles on pelts as long as it doesn't hinder the drying of the pelt.Beaver,fisher,otter and wolf have very heavy saddles and cannot be dried properly unless the saddles are removed,regardless of fat under or not.If drying conditions are good,some wolf can be dried with saddles on.
Graders know there is no damage to hair roots when they feel the saddle weight,or see it on LO pelts when grading.A papery pelt is not what you,the graders or buyers want to see,and this is what you get when saddles are removed from thinner skinned prime pelts.The first thing a grader will do when assessing a pelt is to give it a flip,this will immediately let him know the weight of the skin.(not to be confused with the weight of the fur)Weight is what you want-a prime skin with the saddle intact has a hvy wt skin(supple not boardy),and not papery.Papery is not good.
A little fat under the saddle can easily be pushed out from under with a scud without damaging the saddle.The best tool for this is a dull bone scraper.When there is more fat under the saddle,the saddle will be damaged when scudding out the fat,and it has to be removed at that point.This will determine what is a "little" and what is a "lot".Sections of fur vary,but there are very few pelts in my fur section that have excess fat,although it does ocurr from time to time,with fox and lynx occasionally.Especially if the trapper has been supplying them with beaver for a while.
Saddles left on early skins will leave the skin somewhat boardy,but removing saddles with a fleshing tool on early skins is difficult to do without damaging hair roots.And it wont fool the grader.

Boco, thanks for the great explanation. This is my first year fleshing coyotes. My early ones were blue, but I think I fleshed too close to the hair follicles. Your explanation will really help me. Thanks again.

Hi everyone, I just want to start off saying I'm new to trapping and I'm in need of a bit of help on a fleshing question. I washed my Coyotes by hand in a tub of water with a little dishsoap fleshed the very first one I've ever done or seen done and 3 more after that. I've noticed the last two that I fleshed are now dry and completed but the first two aren't done drying yet on the fleshed side of the hide. I'm thinking I may have missed some fat. What should I do to fix this issue? Is the hide garbage now?

Keep an eye on your pelts as they dry.If you notice any whitish spots that are kind of soft,it is likely fat.You can score those with a knife carefully so as not to dmg the skin underneath,then go over them with a dull scraper or dull knife.You should see the liquid grease come out.Then those spots should start to dry.A fan to keep air moving will help.If the humidity is high you will have problems drying pelts.
I am not a fan of washing pelts especially larger hides like coyote,wolf cats etc.unless they are really bad with mud or blood(which you should prevent in the firstplace).
If you do have to wash the odd pelt,make sure the fur is dry or at least just barely damp before boarding.

I think I got it figured out. I fleshed the saddle off of a couple and felt and heard the krinkly, papery, pelt when fully dried. I also left the saddle on some and felt the thicker, heavier hide on the dried pelt.

I don't know anything about a "scud", but I did find that I could push fat out from under the saddle. I don't know exactly how it happens, but just pushing the fleshing knife over the top of the saddle produces a thick, liquid fat on the blade of the knife. I think the fat is being squeezed up through the saddle rather than being pushed ahead of the fleshing knife and still under the saddle.

This is probably the first year I have fleshed enough coyotes in one year to get a better understanding of what works and what doesn't.

There are a few places where I end up removing some of the saddle - mostly around the armpits just like on a muskrat. There always seems to be enough fat under the saddle there that the saddle comes up easily and it is obvious that the saddle is going to come off when those globs of loose fat are scraped off.

A scud is a dull two handed flesher.