The Olympics help improve the image people have of other countries.
The Olympics help improve the image (that) people have of other countries . It's syntactically fine. The underlined element is a relative clause modifying "image".
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The Olympics help improve the image (that) people have of other countries.
It's syntactically fine. The underlined element is a relative clause modifying "image".
Note that the subordinator "that" is optional, as shown.