長大 【ちょうだい】 (adj-na,n) very long; great length;
頂戴 【ちょうだい】 (aux) (1) please do for me (preceded by -te); (int,vs) (2) reception; being given; get; (vs) (3) to ask for; (P)

So I guess both translations can be applied.

But, if Mega-baa’s meta-tag also removed the data in Densuke that made him guide Yasako to the old cyber-spaces, it could explain a great deal.

Speculating wildly here… A lot of things happened about 5 years back. Yasako’s grandfather died, perhaps leaving his dennou presence in cyberspace. Various children suffered a strange dennou-related illness. Yasako received Densuke and a pair of glasses to go with it. And Yasako’s grandmother started up a missing cyberpet detective agency by recruiting children. Haraken’s aunt was about 12 at the time, and was the first recruit.

But why would Megabaa suddenly want to look for lost pets? Consider: her husband may or may not still exist in cyberspace, perhaps as an Illegal. Illegals may or may not cross back into the real world, or at least into the glasses-accessible world of current-version cyberspace, by taking over the body of a cyberpet. [Some] children are able to locate objects or entities even in out-dated cyberspace (furui kuukan). So it makes a plausible story. Megabaa recruits children from the families of her co-workers, including Haraken’s family; she waits for (or arranges for?) a pet to be lost in out-dated cyberspace; she sends the children out to look for it, hoping that there is an off chance that they will bring back her husband’s cyber-version as a passenger. Some of the children don’t come back…

It will probably make sense that, base on what Yasako said, Illegals and objects within old space are creation of the hidden thoughts among the Imagos. It will explain why an illegal wish to take 4423 in reflection of Isako’s wish. It’s not far fetch since they seem to have a hidden backdoor connection to old space, which might not only allow them to sense, but also leave behind incomplete/corrupted data of themselves. Now if we assume that Kyoko is an Imago (base on how she help Daichi find old space in the past), then it will make sense how the summer festival is stored there base on Kyoko’s perception.

IMO I’m starting to think Densuke was a convenient present from her grandfather. I might be proved quite wrong on this but I’m suspecting perhaps he left some hint or help to her coded within Densuke. After all, she only went and found 4423 and the humanoid Illegal in her youth because Densuke got lost… it’s quite a big stretch but perhaps her grandpa left directions for Densuke to guide her to the right place. And I think it’s worth noting that Densuke’s current design (but not when it was very young, IIRC) has a lock (with a keyhole!) on the collar… wonder if it can be unlocked, and what happens.