The answer to this interesting question is explained in Medea's speech following her interview with Aegeus in which he promises her sanctuary and swears "by the Sun-god's holy beam and by all the host of heaven" to accept her in his land and to never either send her away or "permit any other, one of my foes maybe, to hale me thence if so he will." Once Aegeus exits with the benediction of the Chorus, Medea reveals her thoughts and plans. First, however, let's clarify exactly who Medea asks Jason to persuade.
Certainly, first she ask Jason to "beg Creon to remit [the children's] banishment." He answers pessimistically by saying he doubts whether he can persuade Creon: "I doubt whether I can persuade him ...." Here, Medea changes tactics, which is her intention and plan all along since she is intent on the murder of the bride. Medea now asks Jason to at least "bid thy wife ask her [father] this boon, to remit the exile of the children." Jason here answers with enthusiasm by saying, "Yea, that will I; and her methinks I shall persuade ...." So to clarify your question a bit: Why does Medea ask Jason also to persuade Creusa to let the children stay in Corinth?
Now--after Aegeus grants her sanctuary, Medea explains while the Chorus Leader listens that she will employ her children in her scheme to poison "the king's daughter," Jason's "bride" Creusa: she will poison Creusa through the gifts she will send her that will be delivered by her children, who will act as Medea's emissaries. In other words, her children will carry the poisoned gifts to Creusa.
then will I entreat that here my children may abide, not that I mean to leave them in a hostile land for foes to flout, but that I may slay the king's daughter by guile. For I will send them with gifts in their hands, carrying them unto the bride
The reason the children must carry the gifts to be delivered into Creusa'a own hands is a simple one: Medea spreads a toxic poison on the chaplet and robes that the children deliver to Creusa.
For I will send them with gifts in their hands, carrying them unto the bride ..., a robe of finest woof and a chaplet of gold. And if these ornaments she take and put them on, miserably shall she die, and likewise everyone who touches her; with such fell poisons will I smear my gifts.
Now the logic can clearly be followed so as to understand why Medea asks Jason to persuade Creon and, more importantly, Creusa to let the children stay in Corinth even though she has already decided to kill them. Medea asks this because it is a ruse, a scam, a trick, whereby Medea can murder Creusa even though Medea can't get near her. She will murder Creusa through the poisons overspread on the gifts carefully carried to her by the children.
When the children return, Creusa's death will be eminent and Medea's revenge against Jason begun. Her plan for sanctuary and revenge will be completed when she slays her children for, as she says, "I will slay the children I have borne; there is none shall take them from my toils; ...." Interestingly, Medea's reason for wanting revenge against Jason is a deep one that, according to Medea's conscious, goes all the way back to her marriage to him:
O, I did wrong, that hour I left my father's home, persuaded by that Hellene's words, who now shall pay the penalty, so help me God, Never shall he see again alive the children I bore to him,