Gemara

Sotah 43b (Rav Dimi): R. Eliezer ben Yakov taught that one may not recite Shema Yisrael within four Amos of a corpse - "Lo'eg la'Rash (one who mocks the poor, i.e. the deceased, who cannot perform Mitzvos) Cheref Osehu."

Berachos 18a (Beraisa): One may not walk through a cemetery with Tefilin on his head, or learning from a Sefer Torah in his arm. If he did, he transgressed Lo'eg la'Rash.

R. Chiya and R. Yonasan were walking in a cemetery. R. Yonasan's Techeiles (of his Tzitzis) was showing.

R. Chiya: Lift it up, lest the dead say "today they mock us, and tomorrow they will join us!"

Menachos 41a: Clothes designated for shrouds are exempt from Tzitzis. At the time (when he dies), Raminin Lah (we put on the shrouds) Tzitzis, to avoid Lo'eg la'Rash.

Rishonim

Rif and Rosh (Berachos 11a and 3:5): One may not walk through a cemetery with Tefilin on his head.

Rosh (citing R. Yonah 11a DH Lo): Tefilin and similar Mitzvos are forbidden in a cemetery. Tzitzis is an obligation on the garment. One cannot remove his garment when walking through! R. Chiya objected only because R. Yonasan's Techeiles was on the graves (this is unlike our text). Perhaps this applies only to garments worn the entire day. If one wears a Talis just to fulfill the Mitzvah, this is like Tefilin. He should not wear it in a cemetery, due to Lo'eg la'Rash.

Rif and Rosh (Hilchos Tzitzis (after Menachos) 11b and Siman 9): We put Tzitzis on the shrouds, to avoid Lo'eg la'Rash.

Ba'al ha'Ma'or (Mo'ed Katan 16a DH Aba): Some say that Raminin Lah means that we put Tzitzis on the shrouds. Some explain that we remove them. The former opinion is primary, for it says Raminin Lah (on it), not 'Minah' (from it). The Ri bar Malki Tzedek explains that when carrying the Mes to the grave, we take the Talis designated for shrouds from the casket and put Tzitzis on it. It did not have Tzitzis, for it is merely for honor. At this time, Lo'eg la'Rash applies, for the carriers are wearing Tzitzis. When we bury it with him in the grave, we remove it, to fulfill R. Yochanan's opinion that Mitzvos will be Batel in the future.

Hasagos ha'Ra'avad: We put Tzitzis on the shrouds, but do not tie them on. If Tzitzis were tied to the garment, we untie them. Since there are Tzitzis, the living do not mock the Mes. Since his Tzitzis are not tied, he does not mock other Mesim. We learn from the episode with R. Yonason and R. Chiya that normally, we bury Mesim without Tzitzis.

Rebuttal (Rosh ibid.): We cannot learn from the episode! Even if Mesim have Tzitzis, since they are not fulfilling the Mitzvah, Lo'eg la'Rash applies.

Poskim

Shulchan Aruch (OC 23:1,3 and YD 367:4): One may enter a cemetery or within four Amos of a Mes or grave wearing Tzitzis, as long as they do not drag on the grave, for that is Lo'eg la'Rash. This was when people had Tzitzis in the garments they wore for their needs. Nowadays, we wear Tzitzis only for the Mitzvah. Even if they do not drag, one may wear them only if they are covered.

Beis Yosef (DH v'Ika): Regarding garments worn only for the Mitzvah, R. Yonah did not distinguish whether or not they are covered. However, since the concern is Lo'eg la'Rash, perhaps it is clear that we permit anything covered. The Gemara that forbids going in a cemetery with Tefilin on his head (which are exposed) supports this. We are not concerned for Tefilin on the arm, which are covered. If so, one may enter with a Talis as long as the Tzitzis are covered. The Rashba says that perhaps R. Chiya told R. Yonason to lift and cover his Techeiles. If it is exposed, it is like Tefilin. Hagahos Maimoniyos says that it does not help to cover Tefilin or Tzitzis. One may rely on what I wrote.

Beis Yosef (DH u'Mahari): The Ro'oh (Berachos 18a) says that Lo'eg la'Rash applies to Tefilin, which is a Mitzvah by itself, but not to Tzitzis, which is a Mitzvah of the garment. Mahari ben Chaviv suggests that perhaps the Ro'oh argues with R. Yonah and permits Tzitzis even nowadays, and this is why we are lenient. It is not clear to me that the Ro'oh argues. Rather, we rely on what I wrote, that even R. Yonah permits if they are covered.

Mishnah Berurah (3): If one wears a Talis Katan without a garment over it, he must cover the Tzitzis.

Kaf ha'Chayim (1): The Neshamah of the Mes stands by his grave. If not, we could not distinguish between whether or not the Tzitzis are covered, for in any case it is not in view of the Mes (who is buried)!

Shulchan Aruch (4): Where the custom is to remove Tzitzis from the Mes in the house, if those who carry him wear Tzitzis, there is concern for Lo'eg la'Rash.

Question (Magen Avraham 2): The Shulchan Aruch (YD 351:2) says that the custom is to put Tzitzis on shrouds. Nevertheless we do not enter a cemetery with Tzitzis. This is like the first opinion in the Rosh, that Lo'eg la'Rash applies even if the Mes has Tzitzis, for he does not fulfill the Mitzvah. If so, those who carry the Mes should always be concerned for Lo'eg la'Rash, even if the Mes has Tzitzis!

Answer #1 (Eshel Avraham 2): We can distinguish between those carrying a Mes, and one who goes to a cemetery. (I.e. the former are serving the Mes, so we are concerned for Lo'eg la'Rash only if the Mes has no Tzitzis at all.)

Answer #2 (Kaf ha'Chayim 6): If they made new Tzitzis for the Mes, we are not concerned. If not, we are concerned. Even if he was buried with Tzitzis, perhaps they rotted.

Eshel Avraham (2): A Talis special for prayer is forbidden even if the Tzitzis are covered.

Drishah (1): We forbid only if it is for the Mitzvah and it is over his garments.

Eshel Avraham (2): The Maharit is stringent near a minor's grave, lest the child was an adult (in a previous Gilgul). He permits near a woman's grave, for she was exempt even when alive. He is not concerned lest she was a Gilgul of a man.

Mishnah Berurah (7): The Acharonim concluded that we are concerned for Lo'eg la'Rash even where they do not remove Tzitzis from Mesim.