While searching for Sita, they find a fallen bird drenched in blood. Rama speculates this giant eagle might have tried to swallow Sita and hence struggling in the process. He advances near the bird with the intent of killing it.
Jatayu in it's pitiable condition implores that it's not fair for Rama to kill him as he's already about to die after been vanquished by Ravana.
Jatayu then details about the big fight with Ravana and Sita's kidnap.
Then Rama beheld Jataayu who is akin to a mountaintop in his gleam, and a best beatific brave bird among all the birds, but bloodstained and buckling on earth. [3-67-9b, 10a]
On beholding him who is like a mountaintop in his gleam, Rama said to Lakshmana, "This one has gluttonised Seetha, the princess from Vaidehi, there is no doubt about it... [3-67-10b, 11a]
"It is apparent that this demon skulks in the forest in the semblance of an eagle, and having gluttonised that wide-eyed Seetha he is now reposing comfortably. I will eliminate him with deadly arrows, whose arrowheads blaze away and which shoot off straightly..." Thus Rama declared. [3-67-11b, 12]
On saying thus and on readying a crescent-shaped razor-sharp deadly arrow on his bow, that ireful Rama rushed towards the eagle, as though to a-tremble the whole of the earth that which is within the perimeter of oceans. [3-67-13]
But that bird spewing up frothy blood pathetically appealed to such an ireful son of Dasharatha, namely Rama, in a pathetic tone. [3-67-14]
"Oh, boy Rama, blest is your eternality, for whom you are searching as with the search of a rejuvenescent herb in the vast of forest, Ravana stole that lady and my lives, too... [3-67-15]