9:17 The opinion of some authorities is that the corner where the tzitzis strings are to be inserted, that is, from one to three thumb-widths from the garment’s edge, may not include any seam of threads that are suitable to make tzitzis for the selfsame garment. For example, if the tallis is made of flax, one should not sew there using threads of flax. Rather, he should use, for example, threads of silk. Similarly, one ought not sew with silk threads on the corner of a silk tallis or with wool threads on the corner of a wool tallis. It’s good to defer to this opinion also for the seam that reinforces the hole through which the tzitzis strings are inserted. This opinion, however, only applies to white thread, not to colored thread.
9:18 If one wants to replace a garment’s tztitzis strings with others that are better, or if he wants to replace broken strings with new ones even though the old ones are still valid, this is permissible. The reason one may do this is because he doesn’t intend to cause the mitzvah of tzitzis to cease from the garment ; he’s only removing the existing strings in order to improve the performance of the mitzvah with better strings. In any event, the old strings must be disposed of properly, not casually tossed into the trash.