1
general::
To be returned if not satisfactory, as in They're offering custom-made shoes, manufactured from a computer design, on approval. This expression, applied nearly always to the purchase of goods, was first recorded in 1870.
American Heritage Idioms
2
general::
Phrase(s): on approval
for examination, with the privilege of return. • I ordered the merchandise on approval so I could send it back if I didn’t like it. • Sorry, you can’t buy this on approval. All sales are final.
McGrawhill's American Idioms And Phrasal Verbs