The problem is the value of the TERM environment variable does not match the configured terminal characteristics - specifically the "Home and End keys" and "Function keys and keypad" settings.
These can be hard to get right.
What is expected by the Debian server.
Type infocmp -I to see what your computer is expecting.
$ infocmp -I
# Reconstructed via infocmp from file: /usr/share/terminfo/a/ansi
ansi|ansi/pc-term compatible with color,
…
rmul=\E[m, il1=\E[L, kbs=^H, kcbt=\E[Z, kcud1=\E[B,
khome=\E[H, kich1=\E[L, kcub1=\E[D, kcuf1=\E[C, kcuu1=\E[A,
…
khome=\E[H means that the server expects to receive three characters ESC [ H when you press Home.
You can look at what is expected for other values of TERM
$ infocmp -I xterm
# Reconstructed via infocmp from file: /usr/share/terminfo/x/xterm
xterm|X11 terminal emulator,
…
is2=\E[!p\E[?3;4l\E[4l\E>, il1=\E[L, ka1=\EOw, ka3=\EOu,
kb2=\EOy, kbs=\177, kbeg=\EOE, kc1=\EOq, kc3=\EOs,
kdch1=\E[3~, kcud1=\EOB, kend=\E[4~, kent=\EOM, kf1=\EOP,
kf10=\E[21~, kf11=\E[23~, kf12=\E[24~, kf13=\E[25~,
kf14=\E[26~, kf15=\E[28~, kf16=\E[29~, kf17=\E[31~,
kf18=\E[32~, kf19=\E[33~, kf2=\EOQ, kf20=\E[34~, kf3=\EOR,
kf4=\EOS, kf5=\E[15~, kf6=\E[17~, kf7=\E[18~, kf8=\E[19~,
kf9=\E[20~, khome=\E[1~, kich1=\E[2~, kcub1=\EOD,
kmous=\E[M, knp=\E[6~, kpp=\E[5~, kcuf1=\EOC, kcuu1=\EOA,
…
Here you can see that, if TERM were set to xterm, this server would expect to receive ESC [ 1 ~ when Home is pressed (khome)
If the above is too cryptic, try infocmp -L
You can also do things like tput khome | hexdump -C if you know the terminfo capability names for the keys you are interested in.
$ tput khome | hexdump -C
00000000 1b 5b 48 |.[H|
or, arguably more legibly
$ tput khome | hexdump -e '12/1 "%3_u" "\n"'
esc [ H
or to see what another TERM setting might mean
$ TERM=xterm tput khome | hexdump -e '12/1 "%3_u" "\n"'
esc [ 1 ~
if the output is empty the server thinks that terminal type (TERM) doesn't have that key.
What is actually sent by Putty.
To see what Home actually sends, run vi, press i (for insert mode) press Ctrl+V then press Home and press Esc to exit insert mode.
Solution
Adjust Putty config (or TERM) until what is sent matches what the other end expected.