There are a few different theories around.

But I believe if you look at it logically, you can only
ever end up with the "fixed event" theory.
(thats what I call it, as I dont know its official name)
The past has already happened and is therefore 'fixed', so it cant be 'changed'.
Anything you do in the past has already happened,even if there is no record of it in the future.

So, using your example, yes you can travel back in time to recover a lost object.
But in turn, YOU may be the reason it was lost. Because the 'future' you took it away.
And during the time it was "lost", it wasnt anyWHERE, because it was someWHEN else.

Unless of course the 'future' you stays in the past, in which case, "he" has it, not the 'past' you.

And, of course, the 'future' you will never give the object to the 'past' you
for an unknown reason... Because if he did, then the 'future' you would have
no reason to go back, and therefore was never there to hand it over, an so would
then need to travel back from the future cause its missing again.....
Bzzzzt.... CLICK.... Ping! Paradox Achieved. Thats the unknown reason.


Yes it IS tricky, keeping all the pre- current- and past- tenses in mind,
but you can see the underlying logic.