Sorry to read of your dilemma and see your post go unanswered for coupla days...so I'll stick my neck out and tell ya quick up front that I'm NOT a flooring pro so take this feedback with whatever level of skepticism you wish!
But...
You'll likely have to go either mechanical or 'chemical' route (soften the glue with reaction to something as basic as a WET towel laid on it, then scrape, is a POTENTIAL to try) to remove this glue/burlap residue you're talking about. Since the underlying floor is wood and your goal is its restoration, I'd recommend the mechanical scraping method! (But remember, I'm not a flooring pro! Just someone who's been doing DIY stuff for years.)
Doing a google search for "floor scraper" will yield ya a lot of results...
One such is:
http://www.carpettool.net/scrapers_strippers.asp
Which, has some interesting tools for those who are scraping up VINYL tiles off subflooring, and/or ceramic tiles. Look on down that posted link to near end of the page, and note some of these scrapers go for less than 20 or 30 bucks. You may have some in inventory at local Big Box stores (HD, Lowes) or at local flooring stores.
Good luck to you and here's hoping some of the flooring pros pipe in on this thread!