It's a misunderstanding.
The ring was given by uncle as a reward,
but Sui (the elf girl) misinterpret it,
because when uncle gave it he put it in the her finger.
Before moving into uncle and Sui's relationship...
I had to inform that human race in the isekai world have a handsome or pretty faces.
Everyone of them.
Kinda like a hollywood movie.
Meanwhile Uncle who has an ugly face,
is considered to have an orc-like face by the people of Isekai world.
That's why in the beginning, he always being treated harshly
which make the manga's kinda depressing to read at the beginning chapters.
He always mistakenly seen as an orc, not as a human.
Because of his "ugly" (by isekai world standard) face,
uncle never dreamed he had any chance with girls,
let alone a girl as beautiful as Sui.
It never crossed his mind, not even once.
He didn't realize that elves is a race that could live hundred or thousand years.
something like a face is just a trivial matter for them.
The misunderstanding about the ring was finally resolved later,
which angered Sui and she became bitter and ruder ever since.
This is a scene after Sui knows uncle gave a ring to someone else too :
Perhaps a bit too much spoilers there... but that's fine.
I guess Uncle had self-image issues as a child... though his Isekei would may not be a creation of his imagination, just generic isekei tropes like handsome and sexy people being the norm in medieval times when in truth medieval times were dirty and ugly, even by beauty standards of the time.
Still elves are tip-top sexy in fantasy media so I hope Uncle makes an aunt out of Sue.
