The prayer works. Targum Pseudo-Jonathan on Exodus 8:27 delivers the outcome with plain satisfaction: the Lord did according to the word of the prayer of Mosheh, and removed the swarm of wild beasts from Pharoh, and from his servants, and from his people; not one was left.
Three details deserve attention. First, the word of the prayer of Mosheh. God does not respond to Moses' thought; He responds to Moses' speech. Prayer in the Jewish tradition is verbal, specific, and accountable — a petition spoken into the world, not merely felt.
Second, removed. Earlier plagues ended by natural-sounding means; the frogs died in piles, for instance. This plague ends by evacuation. The wild beasts are lifted back out of Egypt as cleanly as they came in. Creation shifts at the prophet's word.
Third, not one was left. The meturgeman is emphatic. Not one lion in a cellar. Not one wolf under a pile of rubble. Not one scorpion in a servant's shoe. The removal is total.
Why the emphasis? Because Moses is about to find out that Pharaoh will break his word again. A complete mercy is about to meet an incomplete repentance. The meturgeman is setting the stage for the great test of the coming plagues: Pharaoh was given a total, traceable gift from God. He will waste it.
The takeaway: when you ask God to remove something from your life, He can remove every last trace. The question is always what you will do with the relief that follows.