uploading new theme

I had a company make me a new custom theme- based on their recommendation. I was going to use ‘Xtheme’– but they said they would make me a custom theme.
I already had a wordpress site BTW
My site has VERY good google rankings
They were supposed to install the new theme but informed me they cannot do so without moving all my old pictures, picture folders, etc.. which would break the links coming into from Google images.
I have a lot of pics in google images that people use to find my site.

SO – Here is my question. WHY would they say they cannot upload the new theme without deleting my current image folder ? I have been waiting on this new site for months and had SO MANY issues with this company… I am so upset today.