Unfortunately, Google Translate has betrayed you, as it betrays everyone. Truly, there is nothing more treacherous. What it gave you is more like "To restore. Leftovers. Peace."
Restitution is the hard one here: the Latin nouns that mean restitution all mean more like "reclaiming property" - useful in a legal case, not so much in this. However, there are some words that could fit: "Reparatio" means "restoration; renewal"; and "Refectio" means "restoration/repair; remaking; recouping; refreshment; recovery/convalescence". One of these could work. The perfect passive participles (basically, turning a verb into a noun/adjective) "Restitutus" ("Restore; revive; bring back; make good"), "Recuperatus" ("Regain, restore, restore to health; refresh, recuperate") should also work.
For rest, your intuition is closer than Google got it: the Latin noun "Requies" should look perfectly.
But it did get the last word right - "Pax" is, indeed, the Latin noun for peace. One of three ain't... well, it's actually worse than half-bad, come to think of it.
Of course, Latin being what it is, there's some confusion about the cases - Latin has an uncommon vocative case, where a word is being identified (You know when (SPOILERS) Caesar says, "Et tu, Brute?" as he dies? That "Brute" is the vocative of "Brutus".) One could argue that the nominative (naming a word, and the base form of Latin nouns) could also work, because Latin can be singularly complicated.
So! If you prefer the nominative (naming) case: "Reparatio. Requies. Pax."; "Refectio. Requies. Pax."; "Restitutus. Requies. Pax."; and "Recuperatus. Requies. Pax." should work. I'd recommend the third one, as it sounds better to me, but in terms of meaning they're all about equal.
If you prefer the vocative (identifying) case: "Reparatio. Requies. Pax."; "Refectio. Requies. Pax."; "Restitute. Requies. Pax."; and "Recuperate. Requies. Pax." would be correct. ...And yes, the vocative is mostly the same. It's just the two words here where it's different - but I figured it'd be better to be too accurate, than not enough.