Theory:

‘I’ve found it!’ she cried. ‘I’ve found something!’
 
And now, barefoot, she ran breathlessly towards him, in her outstretched hand a rusty old medal.

He took it from her and turned it over on his palm.

‘Is it the Iron Cross?’ she asked eagerly.

‘Yes’, he said, ‘this is it.’

‘Now I know why you came. You wanted to see if it was still in the tree.’

‘You may be right. I’m not really sure why I came. But you can keep the Cross. You found it, after all.’
Explanation:
 
The girl climbed the tree and found something; she was very excited. She shouted out that she had found something.

She did not wear her slippers. She just ran barefoot towards the man and showed him a rusty old medal.

The man took the medal in his hand and saw it over and over again.

The girl asked if this was the Iron cross, that he had cited.

The man said, yes, this is the one.

The girl said childishly, "Now I understand why you have come. You just wanted to see if the cross was still there in the tree."

The man said that he was not sure why he has come, but she can keep the cross as she had found it.
Meanings of difficult words:
 
Number
Word
Meanings
1.
 Outstretched  Extend or stretch out.
2.
 Rusty  Corroded.
3.
 Eagerly In a keenly expectant or interested manner.
4.
 Breathlessly  In a way that is characterized by great excitement.
Reference:
State Council of Educational Research and Training (2018). Term-1 English Standard-9. I Can’t Climb Trees Anymore - Ruskin Bond (Slightly adapted) (pp. 157-160). Published by the Tamil Nadu Textbook and Educational Services Corporation.