Spiffy new terminal emulators seem to come with their own terminfo definitions. Venerable hosts that I ssh into tend not to know about those. kitty comes with a thing to transfer that definition, but it breaks if the remote host is running tcsh (don't ask). Similary the one liner for alacritty on the arch wiki seems to assume the remote shell is bash. Forthwith, a dumb shell script that works to send the terminfo of the current terminal emulator to the remote host.

EDIT: Jakub Wilk worked out this can be replaced with the oneliner

infocmp | ssh $host tic -x -

#!/bin/sh

if [ "$#" -ne 1 ]; then
    printf "usage: sendterminfo host\n"
    exit 1
fi

host="$1"
filename=$(mktemp terminfoXXXXXX)

cleanup () {
    rm "$filename"
}

trap cleanup EXIT

infocmp > "$filename"

remotefile=$(ssh "$host" mktemp)

scp -q "$filename" "$host:$remotefile"
ssh "$host" "tic -x \"$remotefile\""
ssh "$host" rm "$remotefile"