I remember when my kids were little, I washed everything before they put on clothes. Now I'm not so hyper-vigilant, but I do notice funny odors in linens, towels, clothes, evereything you buy. Just normal use and washing will eventually lift the smell.

What is a "hessian-like smell".
Linen, even new linen smells like the detergent it's been washed in.
Linda c

Sorry, I think hessian is similar or the same as what you call burlap?

Because linen is also an organic fiber it will have a similar smell to what you describe. That's not exactly a bad thing. I wouldn't worry, it will work out and start smelling like everything else in short order.

I wash everything that's washable before I use it. Never used to but now so many things are imported with chemicals sprayed with crap to kill bugs, etc., and so many things have the manufacturers' DNA on them -- just wash it before you use it. I once worked for a fabric store chain -- we received bolts of fabric from India that felt oily and smelled so rancid that it was pulled and returned. My advice -- wash it and if you still question whether or not you want to use it -- TAKE IT BACK.