Could you please tell me how to say “Reward offered if returned” in the above-mentioned languages?
Swedish:
“Återlämnas mot belöning” is the standard phrasing, IIRC. I’ll have a look at the others.
ETA: hang on, I may have misread. “Belöning utlovas mot återlämning” is probably better. The first one is if you have found something and want a reward. My bad.
I’m not having much luck with my online dictionaries and phrasebooks, sorry. The Swedish - Danish translator I tried offered “The reward promised to return”. You should be able to skip Danish though since it’s similar enough to Swedish, or just wait for Rune or one of the other Danes to help out.
German was worse.
Filling in some of the grammatical blanks got me the German “Belohnung angeboten für sichere Übertragung zurück zu Inhaber,” which translates back to English as “Reward offered for safe transmission back for owner.” 
A shorter German for would be “Belohnung bei Rückgabe.”, but “Rückgabe” implies that the object has been taken rather than found - what’s the context?
We might be talking about a Canadian vs. American dialect dichotomy, but I’ve never seen wording as stated by the OP, since one wouldn’t want to reward the person who stole the item. Instead one would want to convey that there will be a reward if the item is turned in, although it’s certainly possible that the person who turns it in is the same person who took it. but the way I usually see such announcements worded is some variation on “LOST (ITEM)” followed by one of the following, or similar, as appropriate:
[ul]
[li]“Reward If Found” - implies hoped-for restoration to owner by innocent finder. [/li][li]“No Questions Asked” - implies item is being withheld by an intentional thief, but promises there will be no trouble for them if they turn it in[/li][/ul]
I’ve never seen “Reward If Returned”. If you take someone else’s lost or forgotten item innocently, with the intent to turn it in to a lost-and-found for the owner’s benefit, then you’re not returning it. Now I’m really going to split hairs, but this is where language and grammar really do get interesting rather than all the pedantry and debates over prescriptivism (and in which I have been fully engaged. 
). If I take your lost item with the intent of keeping it safe and restoring it to you, I wouldn’t call that returning either. To my ears, “returning” something to someone implies that I took it from that person, or from his things.
Sorry to the OP for the hijack, but you raised an interesting question.
If you are missing something you lost, and want to express that you will give money to the one who finds it and returns it, in Swedish, the key word is “hittelön” - ‘finder’s reward’, I guess.
For instance: “I lost my wallet at Wal Mart - I’ll pay anybody who finds it, and returns it”, would be:
Jag tappade min plånbok på Wal Mart - Hittelön!
Claptree’s* “Belöning utlovas mot återlämning” *is another way of saying “Hittelön”, but a more formal way of expressing it (which might be good); but “återlämning”, to me, sort of implies that the person who returns it, is the one who took it (“åter” being “back”, and “lämning” being “give”); while “hittelön” implies that the one who returns it, is a preson who happen to find it (“hitte” meaning “found”, and “lön” being “reward”).
But since Claptree too is from Sweden (Hej kompis!), I’m not arguing, just adding.
In Dutch, the typical phrase in situations would be ‘de eerlijke vinder wordt beloond’ - the honest finder will be rewarded. This would apply in situation in which something was lost rather than stolen. Of course, if it was stolen and then discarded, than you could also use it. Even if the thief grew remorseful, and became an eerlijke vinder, it might work because you wouldn’t ever know. If, however, you’re making a direct appeal to the thief, you would need to be saying something else.
In Swedish I would use the term: “Hittelön utlovas”.