The resurrection accounts in the New Testament include some details that are embarrassing or unusual and, therefore, are less likely to be fabricated. I discuss several examples in the post just linked. I want to elaborate on one of them here.
As I mentioned in the post linked above, ancient Jewish depictions of resurrected and other exalted individuals often portray them in a glorified body different than the more ordinary body Jesus has in the gospels' resurrection accounts. The gospels not only portray the resurrected Jesus as if he has an ordinary appearance, but even refer to his crucifixion wounds as still present (Luke 24:39-40, John 20:20, 20:25-7). Since resurrection is associated with healing, it would be unusual if even one of the gospels portrayed Jesus as retaining his wounds. That two gospels mention it is even more significant. It's not something we'd expect if the gospel authors or their sources were independently making up stories in accordance with the common expectations of their culture, for example.
Given what Isaiah 26, Ezekiel 37, Daniel 12, and other pre-Christian Jewish sources tell us about resurrection and what the earliest Christian sources tell us, would we expect Jesus to have retained his crucifixion wounds? If the gospel authors or their sources were making up stories during the time when Paul was writing his letters or shortly after, would we expect them to portray the resurrected Jesus as they do?
Consider what Paul says about resurrection. It occurs "in a moment, in the twinkling of an eye" (1 Corinthians 15:52). By that standard, Luke 24 and John 20 wouldn't be referring to a gradual resurrection. They wouldn't be thinking that the crucifixion wounds were still present because the resurrection process wasn't completed yet. (And the gospels repeatedly refer to how Jesus has been raised, as an event that's already finished.) Paul tells us that the body "is sown in dishonor, it is raised in glory; it is sown in weakness, it is raised in power" (1 Corinthians 15:43). Attaining a resurrection body is likened to putting on imperishability and death being swallowed up (1 Corinthians 15:53-4), both of which suggest a covering up of death. The "putting on" terminology is the language of putting on clothing. If clothes have been put on, which should cover up any signs of death, and death is concealed by being swallowed up, you wouldn't expect to still see crucifixion wounds. Elsewhere, Paul refers to how Jesus "will transform the body of our humble state into conformity with the body of his glory" (Philippians 3:21). Again, notice the contrast between current human bodies and Jesus' glorious resurrection body. Similarly, Hebrews refers to how Jesus has "the power of an indestructible life" (7:16).
While such descriptions of the resurrection body don't contradict what we see in the gospels, they underdetermine what we see there. You wouldn't portray Jesus as he's portrayed in the gospels if all you had to go by were passages like the ones I've just cited. You wouldn't include details as potentially misleading as Jesus' retention of crucifixion wounds. The best explanation for why Luke and John refer to Jesus' having those wounds is that the early Christians encountered the risen Jesus that way, even though that experience was different than what was expected and fits so awkwardly with the mainstream view of resurrection that we see in pre-Christian and early Christian sources.
I want to address a potential objection. What if Luke, John, or their sources made up the accounts of Jesus' retention of his crucifixion wounds in order to argue for the continuity of the pre-resurrection and post-resurrection bodies?
There are a lot of other ways to argue for continuity. You wouldn't have to make up accounts about wounds being retained, along with all of the difficulties that accompany that kind of scenario. Luke and John had already presented evidence for continuity, such as the empty tomb and conversations the risen Jesus had with people who knew him before his death. Anybody close enough to him to examine his wounds could also identify him by the rest of his body, his voice, what he said, etc. The wounds are evidence of his identity, but among many other lines of evidence. That even one of the gospel authors thought he needed to make up a retaining of crucifixion wounds in order to argue for continuity is unlikely. That both authors thought they needed another argument for continuity, and both made up the same unusual and difficult argument for it (that Jesus still had crucifixion wounds), is even more unlikely.
Furthermore, two of the three passages in question (Luke 24:39-40, John 20:20) don't even mention the wounds. They just mention the body parts involved, leaving it to the reader to infer that the wounds are in mind. Elsewhere in both gospels, people have difficulty identifying Jesus (Luke 24:13-35, John 20:14, 21:4). That isn't the sort of content you'd expect authors to include if they were willing to fabricate accounts of Jesus' retaining his crucifixion wounds in order to argue for the continuity of his body. If Luke and John were being dishonest, it's doubtful that they'd be so subtle and inconsistent about it.