In one of the Lakewood weekly (free) papers, I recently came across an ad from Rabbi Yehuda Shain in which he notes that jute twine is acceptable to tie and hold down schach. Keeping the lecatchila din of only using something you would use for schach in order to fasten the schach in mind, is jute twine not mekabel tum'ah? Would one be allowed to use it as schach? The following is what I found after a google search: in this responsum the OU discusses hemp and cotton strings. We can probably assume that the same applies for jute. But I am still looking for sources - mekoros discussing the acceptance of jute or other "gidulei karka" strings for fastening schach.
From Star K
In addition, l’chatchila, kosher schach may not be supported by anything which is mekabel tumah (see Rama O.C. 629:7). According to the opinion of Rashi (as brought in Shaar Hatziyun 629:20) spun or woven threads (e.g. string, yarn) are mekabel tumah. Rav Moshe Feinstein states (Igros Moshe, O.C. 1:177) based on a Mishna, if something which is mekabel tumah is used to hold wooden slats together, the slats themselves are also mekabel tumah and are no longer kosher for schach use. Therefore, Rav Moshe Feinstein explains that wooden venetian blinds held together with cloth tape or string are not kosher for schach. It follows that according to Rashi bamboo slats held together by multi-filament cord (i.e. it is braided or twisted) are also not kosher for schach (even if they are not made to sit or walk on).
However, monofilament (commonly used for fishing line) is not woven or spun material. Therefore, it is not mekabel tumah and may be used to hold bamboo slats together. All Star-K certified bamboo schach is held together with monofilament cord.
So, if the jute twine is spun or woven, it might be problematic. It seems that the Jute fabric is spun and woven, so if the twine came from fabric it would be a problem. If it’s straight jute without any spinning or wearing it should be fine.