The NWT is reminiscent of Johannes Greber's dubious translation: "The earth quaked, and the rocks were shattered. Tombs were laid open, and many bodies of those buried there were tossed upright. In this posture they projected from the graves and were seen by many who passed by the place on their way back to the city" (The New Testament -- A New Translation, 1937). The NWT follows Greber's lead and also imposes parantheses to artificially mark part of the text as a digression:
"The earth quaked, and the rock-masses were split. And the memorial tombs were opened and many bodies of the holy ones that had fallen asleep were raised up, (and persons, coming out from among the memorial tombs after his being raised up, entered into the holy city,) and they became visible to many people."
In both readings the bodies in the graves are not resurrected but merely "raised up" or "tossed upright" and remained in their tombs, while other persons walking among the tombs went into the city (not those tossed upright in the tombs). This is a very contrived interpretation that can be criticized on a number of grounds.
First we read that "tombs were opened" (mnèmeia aneòkhthèsan), and this is an allusion to the Vision of Dry Bones (a primary OT source on the resurrection belief) where God says " I will open your tombs (anoig ò hum ò n ta mn è mata) and cause you to come up (anax ò ) out of your tombs (ek t ò n mn è mat ò n), my people; and I will bring you into (eisax ò hu mas) the land of Israel" (Ezekiel 37:12 LXX); both anoig ò and aneòkhthèsan are forms of the verb anoigein "to open up" (first person singular active present and third person plural passive aorist, respectively). The two words occur elsewhere in descriptions of the resurrection: "And after these things a trumpet blast, and the tombs will be opened (mnèmeia anoikhthesontai) and the dead will rise up uncorrupted" (Greek Apocalypse of Ezra 4:36).
Second, the Greber translation and the NWT refer only the bodies being "raised up" or "tossed upright", and Greber further adds a reference to "this posture". But this ignores what is stated in text itself. The verb egerein is here used in reference to bodies of those who said to be kekoimèmenòn "sleeping". This refers to the state of death from which the dead are awakened and raised up. One may compare the story of Lazarus; Jesus says that he was going to wake up (exunipzein) Lazarus who "has fallen asleep" (kekoimètai), such that he "will rise again (anastèsetai)" (John 11:11-12, 23), or Paul stating that Jesus "has been raised" (egègertai) from the dead as the firstfruits of "those of have fallen asleep (kekoimèmenòn)" (1 Corinthians 15:20). Also a nominal form (egersin) of the same word (egerein "to rise up") is used in the next verse (v. 53) to refer to Jesus' resurrection (although it seems that this reference is an interpolated gloss, see below). It thus should be understood as resurrection in the preceding verse.
Third, v. 53 attributes to following actions to the holy ones: they "came out" (exelthontes, masculine plural in agreement with "holy ones" in v. 52) of the tombs, they "came into" (eisèlthon) the city, and then they "appeared" (enephainisthèsan) to many. These actions presume an agency not attributable to inanimate bodies, not even by assuming that others picked them up and carried them into the city. This motivates the NWT's parenthetical insertion of "persons" into the text to make the reference to the first two actions attributable to conscious agents, even tho there is no basis for "persons" in the text.
Another contrivance is the statement that these persons were "coming out from among the memorial tombs" in the NWT, which implies they were on the surface walking between the tombs, whereas they clearly are exiting the tombs themselves (exelthontes ex tòn mnèmeiòn "came out from the tombs"). And this language is clearly borrowed from Ezekiel 37:12 LXX: After opening the tombs, Yahweh would " cause you to come up (anax ò ) out of your tombs (ek t ò n mn è mat ò n)" , and then he would "bring you into" (eisaxò) the land of Israel. This is parallel to the opening of the tombs being followed by the dead "coming out" (exerkhomai) "out of the tombs" (ex tòn mnèmeiòn) and then "coming into" (eiserkhomai) the holy city. So the passage in its construction is clearly a resurrection narrative, and the Greber and NWT renderings attempt to mitigate this.
Finally, the words meta tèn egersin autou "after his resurrection" in v. 53 has the appearance of an awkward gloss. It introduces a contrivance: the dead are raised at the moment the temple veil is torn but they inexplicably wait in their graves until Easter Sunday, and the Matthean account has the centurion exclaim "This was the son of God" in amazement in the very next verse. The centurion is not only commenting on the earthquake, but "the earthquake and the things that happened". The spectacle of the dead rising from the graves and walking into Jerusalem was certainly "the things that happened" following the quake. The gloss interferes with this reading. It has a clear theological motivation; Paul wrote: "But Christ has in fact been raised from the dead, the first-fruits of all who have fallen asleep...All men will be brought to life in Christ but all of them in their proper order: Christ as the first-fruits and then after the coming of Christ, those who belong to him" (1 Corinthians 15:20-23). This would explain why the text was glossed: Christ must first rise and leave his tomb prior to the saints, who only do so "after his resurrection". The gloss however is only partly successful in harmonizing the Matthean story with Paul since the account would still have the resurrection of the dead occur prior to that of Jesus.
One might also wonder if the tradition underlying the passage is relevant to the claim by Hymenaeus and Philetus that "the resurrection has already taken place" (2 Timothy 2:16-17), a claim that the Paulinist author of the Pastorals rejected.