May one tie a Gartel to a Sefer Torah?
Some Poskim rule that when it is done in a way that one makes a bow over a knot then it may only be done to undo that day, such as to undo by Mincha. If however one will not be using the Sefer Torah until Monday or later, as is the case when reading after Mincha, then doing so is forbidden. Rather one is to fasten the ends into the binding.
Untying the Gartel: If the Gartel of a Sefer Torah has been tied in a way that is forbidden to undo on Shabbos, such as a double knot or a bow over a knot, then it is likewise disputed whether it may be untied. Some Poskim rule that if another Torah scroll is available then one is to take it out. Others however rule that there is no need to return the Sefer Torah and remove another one, and one may thus undo the knot even if it is a double knot.
If one took out the Sefer Torah and found that it was tied with a double knot may it be undone?
See above regarding the dispute. The Ketzos Hashulchan rules that one may untie it and does not need to take out another scroll.
 Minchas Shabbos; Minchas Yitzchak 8/19. Beir Moshe quoted in Piskeiy Teshuvos 317 footnote 19. Mentioned in Betzeil Hachachma 3/112.
Seemingly they do not permit this on the basis that it is being done for the sake of a Mitzvah being that it is possible to not tie it at all.
 As rules Admur in 317/1 that it is only permitted to make even an amateur knot when doing so to undo that day.
 Ketzos Hashulchan 123 footnote 9; Shut Mahrshag 60 although in his conclusion he suggests to be stringent although not to protest against those which are lenient. Rav SZ”A in SSH”K 15 footnote 178 says the custom is to be lenient.
 Because doing so is considered an honor for the Sefer Torah, and any knot which is only Rabinically forbidden is allowed to be done for a Mitzvah. However it is honorable to merely stick the endings into the binding was suggested above. [ibid]
This is also implied from the ruling of Admur in chapter 651/6 that Admur rules that by a Lulav such a knot may not be made because one never plans to untie it. Thus implying that if done to eventually untie is allowed because doing so is a Mitzvah. [so learns also Ketzos Hashulchan ibid; Shut Mahrshag ibid]
 On the one hand one can claim that according to all it would be forbidden when done with intent to undo that day as since one can tie it in a permitted way which is by making a bow over a knot, it is no longer considered a need for a Mitzvah. If however it is done after Mincha, to be undone 2 days later, then since whatever knot one makes is the same Rabbinical prohibition, which may be done for the sake of a Mitzvah then there is no difference in regards to which knot one makes, and so rules Shut Mahrshag 1/60 that one is not to protest over one who makes a double knot.
 Kaf Hachayim in name of Ruach Chayim, brought in Ketzos Hashulchan ibid; following the above mentioned Poskim which are stringent regarding tying the Gartel on Shabbos. However if no other Sefer Torah is available then obviously according to all one may untie it, as it is for the need of a Mitzvah.
 Ketzos Hashulchan ibid
 As one is doing so for the sake of a Mitzvah.
 123 footnote 9