Quick Answer: In the ending of The Gift, Gordo reveals his final gift to Simon and Robyn: a video of him drugging and presumably assaulting Robyn. It is unclear whether or not Robyn’s baby is Gordo’s or Simon’s, but Gordo gives the hint, “It’s all in the eyes, you see.” Since Gordo has brown eyes and Simon has blue eyes, we can guess the father by checking the baby's eye color. When Simon runs back into the hospital to see Robyn and the baby, we cannot clearly identify the baby’s eye color, but it doesn’t matter. Since Gordo relies on psychological manipulation rather than physical, it’s likely that he did not assault Robyn and made up the lie to echo Simon’s fabricated story that Gordo was molested as a child.
In The Gift (2015), married couple Robyn (Rebecca Hall) and Simon Callem (Jason Bateman) are persistently visited by the seemingly menacing Gordo (Joel Edgerton), Simon’s former classmate. While Gordo's actions and intentions seem highly disturbing, by the end we learn key information that may reverse our sympathies: as a child, Gordo was the victim of Simon's bullying.
During their teenage years, Simon fabricated a story about how Gordo was molested by an older boy, which ultimately ruined Gordo's family and life. But just when we begin to despise Simon and forgive some of Gordo’s bizarre behavior, we see Gordo’s final gift to the Callems: a video of him drugging and presumably assaulting Robyn.
Simon (Jason Bateman) watches Gordo's (Joel Edgerton) final video
Simon begins to doubt whether or not he is the father of Robyn’s baby and quickly goes to the hospital to check on his wife, only to see Gordo by the hospital elevators. Gordo escapes before Simon catches him but later calls Simon to suggest that Simon may or may not be the father. At the end of the phone call, Gordo hints, “It’s all in the eyes, you see.” Simon desperately goes back into the hospital to see the baby. As Simon struggles to see the baby, it isn’t clear if the baby has Gordo’s brown eyes or Simon’s blue eyes. The movie’s audience seems to be split on the matter; some of them think the baby has blue eyes while others think the baby has brown eyes. However, it doesn’t matter what color the baby’s eyes are because the baby isn't Gordo's final gift.
Robyn (Rebecca Hall) holding her baby, whose eye color is indistinguishable
Even though Gordo suggests that the baby is his, it is much more likely that the baby is actually Simon’s. Gordo relies on emotional and psychological manipulation, not physical. Therefore, it would be out of character for him to suddenly assault Robyn when there is no evidence that he would ever be physically violent against her in the first place.
It is also important to note that Gordo’s story heavily parallels the fabricated story Simon made about Gordo being molested. Gordo could be creating a similarly fictional story to make it seem that Robyn was assaulted as revenge for Simon’s bullying — the act of inventing the story creates severe mental disturbance for Simon, without the event needing to occur. If Gordo actually assaulted Robyn, on the other hand, this would be an extreme act of violence out of proportion with Simon's wrong, which harms Robyn far more than her husband.
The film's ending implies that Gordo is more interested in making Simon understand what he did as a childhood bully. During the same phone call at the hospital, Gordo tells Simon, “You see what happens when you poison other people’s mind with ideas?” Gordo crafted a story that would ruin Simon, and now Simon has to live with the consequences of Gordo’s lies the way Gordo suffered from Simon’s lies. Although one can argue that Simon can always get a paternity test done and resolve his anxieties, that would involve telling Robyn that she may have been assaulted, which could ultimately be a lie. Robyn also has brown eyes, so it's more likely that, regardless of his father, the child will also have brown eyes, feeding Simon's doubts. Since Simon doesn’t know whether or not Gordo is telling the truth, the only way he can preserve what is left of his relationship with Robyn is to remain trapped in Gordo’s fabricated story, never knowing for certain what is true. The final gift Gordo gives to Simon is not the baby but the lie that seals Gordo's revenge and forever destroys Simon's chance of a peaceful, happy life with his family.