What do the dead remember?
What is the meaning and function of ἀλλὰ?
Eurip. IA 1238-1240
βλέψον πρὸς ἡμᾶς, ὄμμα δὸς φίλημά τε,
ἵν' ἀλλὰ τοῦτο κατθανοῦσ' ἔχω σέθεν
μνημεῖον, ἢν μὴ τοῖς ἐμοῖς πεισθῆις λόγοις.
Another poet weighs in on the question:Look at me, give me your glance and your kiss so that when I have died I may at least have that to remember you by, if you are not moved by my words.
David Kovacs 2002.
I consulted the first chapter of Robert Garland “The Power and Status of the Dead” which wasn’t conclusive. It appears that the cognitive powers of the dead were considered by some to be quite limited or none at all. I looked in Helma Dik (Word Order 2007) which has a chapter devoted to Greek ways of dying. Again nothing conclusive.“If ya give this man a ride, Sweet memory will die
Killer on the road” Jim Morrison
Riders on the Storm 1971.
Then I consulted the Bryn Mawr “commentary” on Eurip. IA. They had a cryptic note on ἀλλὰ “at least” GP 12. Cooper has a whole page on this with many examples including Eurip. IA 1239 cited twice.
This is also a NT idiom. See F. Danker (BDAG p45, ἀλλὰ #4).In the apodosis of a conditional [...] sentence ἀλλὰ means contrariwise, on the other hand, still. After Homer, the apodosis is typically a less desirable alternative [...] as a fixture in this recurrent structure ἀλλὰ developed a special sense which it exhibits when standing alone and when there is continuous discourse. It can suggest an abbreviated or omitted apodosis: at least, at any rate. 
There is a third question we could address: Why is the apodosis fronted? In other words, why do we see
ἵν' ἀλλὰ τοῦτο κατθανοῦσ' ἔχω σέθεν μνημεῖον in front of the conditional ἢν μὴ τοῖς ἐμοῖς πεισθῆις λόγοις?
Robert Garland, chapter one from The Greek way of death Cornell University Press 1985.
 Denniston’s Greek Particles page 12. Looked at this in google books. Denniston is cryptic and unhelpful.
 Guy L. Cooper III, Greek Syntax, vol 4, page 2858, 2:69.5.5.A&B.