I think it's ok that when the gifted subs run out, you can't show the gifter badge in chat anymore, just like if your sub runs out, you can't show your sub badge. But at least make it so that if someone clicks on your name, they can see that you have previously gifted subs in this channel. Like with your own sub, when it runs out it will still say 'previously subbed for X months'. But with gifted subs, it's currently not possible to tell if someone has previously gifted subs in the channel after they run out.
I think it's ok that when the gifted subs run out, you can't show the gifter badge in chat anymore, just like if your sub runs out, you can't show your sub badge. But at least make it so that if someone clicks on your name, they can see that you have previously gifted subs in this channel. Like with your own sub, when it runs out it will still say 'previously subbed for X months'. But with gifted subs, it's currently not possible to tell if someone has previously gifted subs in the channel after they run out.