The Shulhan Aruch rules in Siman 15 that, in general, one may not remove the Sisit from a Tallit, since this is considered to the Tallit. However, if the intent of removing the strings is to retie them to another Tallit, it is permitted. He may even remove the strings from a Tallit that is obligated M'Doraita (from Torah law), such as a wool garment, and retie them on a garment that is only obligated M'Drabanan (from Rabbinic law).
There are two conditions to this leniency. First, the new Tallit must be in front of him when he unties the Sisit from the old garment. Otherwise, the Hachamim were concerned that he would remove the Sisit and not have the opportunity to acquire the new garment. Second, the Mishna Berura (Rav Yisrael Meir Kagan of Radin, 1839-1933) quotes the Peri Megadim that one may only remove Sisit from an old Tallit to tie on a new one, if he has no other available strings. However, today, when it is so easy to buy strings, one should leave the old strings on the old Tallit.
There are exceptions to this rule in which it would be permissible to remove Sisit, even if the intent is not to retie them. First, if one is selling the garment to a non-Jew, he should remove the Sisit. Also, if one wanted to replace the old Sisit with more Mehudar strings, he is allowed to do so, even if the old strings are still Kosher. For example, if one string ripped, the Sisit are still Kosher, but he didn't want to wear Sisit with only 31 strings; he wanted to wear the complete Misva.
SUMMARY:
One may not remove the Sisit from a Tallit unless he intends to retie them on another garment that is immediately available and there are no other strings available, he intends to sell the garment to a non-Jew or he wants to replace them with more Mehudar strings.
