Since you've had no replies from others, I'll offer my opinions.
I would soak the cheesecloth in rainwater or dechlorinated water first. If you had a batch of Horse Manure tea, that might be a good soaking solution. I use HM Tea , which I keep aerated, for all kinds of mitigating purposes. I use paint strainer bags: They cost about $2 each at Home Depot. They have a little elastic and wash well in the rain barrel.

However: I wouldn't strain the pureed food before feeding the worms. I think others would disagree, but I think if you have a good draining system, you might as well introduce it all into the ecology. In my case the liquid can go in the HM bucket for aeration and it can be used again -- whether to give the blender enough liquid or the bin a shot of moisture.

I hesitated to answer because I was stuck on why a person would want to remove the liquid from pureed food when many nutrients would be lost from the food in the liquid.

I think EdKinAZ wants brand new clean cheesecloth touching the food not rainwater or HM rinsed cheesecloth :-) and is possibly concerned with dioxins used in the cheesecloth bleaching process harming the worms. I would say if you are not concerned with it touching the food then I would not worry about it touching the worm bin. I bet cheesecloth could be the only bedding ever used and it might only slow the bin down a little. Might not want to eat the dioxin filled worms. Possibly they make non bleached cheesecloth? Possibly use a bleached or non bleached coffee filter to drain out some of the liquid. Possibly push the food up one side of the bowl and just pour out the liquid you do not want. I take it the liquid is what you are putting into the bin. Or I could be confused. I am glad you are at least getting some use out of it. The worms will love it. Cheesecloth unless you have a years old mega stash of it is super expensive like two dollars for enough to filter one little thing. Weird but cheesecloth is out of my price range.

You may be interested in a juicer. Fiber out one tube and juice out the other.