Just a heads up, but are you sure he's not asking for a Cerebral Booster and a Mnemonic Enhancer? Synaptic Booster is the reaction enhancer/initiative booster (and is also .5 Essence per level, which is pure murder on the Magic/Resonance for those who care about that sort of thing). Cerebral Booster [3] and Mnemonic Enhancer [3], conversely, would give him a +3 to Logic and +3 dice on memory related tests (which he would no doubt insist was pretty much everything), while still sneaking in at 0.9 Essence.
Either way, though, the answer is to just say "No, you don't get free stuff for cooking up a backstory. A backstory is how you justify to yourself and the GM to have the stuff you pay for, like normal, during character generation. Yes, your Tir-centric backstory is fine for justifying the purchase of some Bioware. But if you want to buy the Bioware, you follow the rules for buying Bioware, assign the right Resources, and stick within the Availability limits of the campaign." He can buy them at up to rating 2 like everyone else (limited by Avail), and he can figure out how to shuffle points and pony up the cash for them like everyone else, too.
Also, I would explain to him that Paragons don't really exist in 5E yet, so if he wants to he can squat on some karma until they come out (but that no, he can't just neatly port over one from 4E to 5E).
And shame on him for trying to use the Tir to weasel into this many free points.