Soak the seeds in water for 15-20 min so that the mucilage swells, thereafter rub the seeds on filter paper/ sand paper/ any other coarse paper. The mucilage will be removed. Good Luck!!

I think formation of gel like structure does not hurdle in seed germination. However if you treat the gel coated seeds with alkali, that can be removed. I this case you should adjust alkali concentration and time according to seed capability

The mucilage will be removed with alkali but you should adjust concentration

The outer layer of mucilage is loosely attached, so it can be remove by vigorous shaking or any chemical treatment like alkali / EDTA. But it is difficult to remove the inner layer.

If you soak the seeds for different times (1 hr in hot HCl  or upto 24, 48 hours or more i HCl at different increasing normalities, mucilage  (polysaccharide only or with proteins will get hydrolysed and becomes soluble) this dissolved mucilage may be concentrated to desired levels;

When I have used seeds that produce a mucilage when moistened, I have removed the mucilage using scalpel and forceps under a dissecting microscope. In a laminar flow if the seeds have been sterilised.

Soak the seeds in  1% Sodium hypochlorite for 15-20 min and then wash with water.

I agree with Mr. Bhat.  After appliying the optimum surface sterilization protocol immerse the seeds in sterilized water for some time (1 hr to 24 hr) depending the size of the seeds. and then use scalpel and forceps to isolate kernels from hard shelled seeds under a dissecting microscope. 

I had the same issue with tomato seeds so what I did was placing them in mild water for around 30 minutes then drain and dry them with a soft towel after that placed in a dry and quite warm place to get dry however I noticed the germination wasn't what it supposed to be, so I believe it is better to place them in a can or a container mix them with something sharp like broken glasses then shake it as its dry especially if your place is humid. 

i have been experimenting with different soak time and concentrations of sodium bicarbonate as a pre-sterilization soak. I read somewhere about a .1 M bicarbonate soak for 12 hours and this has worked for some seeds like fenugreek very well. I am still trying to adjust it properly for basil seeds. I tried Chia seed (from the grocer) as a proxy for basil due to similarity in size but when I compared the two after pre soaking and sanitizing (ruthenian red stain) the basil mucilage was still very much intact with near 24 hours at the .1M concentration. if you wish to experiment with this, depending on the size of your seed use a shaker or a multiple microfuge attachment to a vortex and different concentrations of sodium bicarbonate solution, rinse thoroughly, and apply a .1 to .5 ruthenian red stain and look under the dissecting scope to see how much mucilage layer has broken down. the red will be most intense in areas where pectin is concentrated. If you have pectinase you can also try a similar experiment to try and dissolve only the outer layers of the seed and not the contents. if you use chia seeds to practice your procedure with be aware that most of the ones in the grocery stores are heat sterilized (to kill bacteria that cause food poisoning symptoms) and will not germinate

Ammar, you did not say what species you are working with. For tomato, for instance, fresh harvest seeds I let them on an cup with water for 3 days, then wash and sterilizes with NaOCl ...