HC-06 resends last message on connection loss

The remote controls for my TV and Satellite box are failing, so I made a new remote that uses Bluetooth rather than IR.

The keypad uses an STM32C103C8T6 (Blue Pill) and an HC-05, and sends the 4-byte code. The receiver uses an Arduino Pro Mini and HC-06, and feeds it to the irremote library.

It works quite well, but has a rather annoying behavior when the keypad is turned off to save its battery.

20 seconds after the keypad is turned off, the receiver's HC-06 starts blinking rapidly indicating it's waiting for a connection. At that time it appears to send to the Pro Mini the last message again, followed by 2 messages containing a single 'c'. If the last command was to turn off the TV, it gets turned on again!

The workaround is to make sure the last button pressed does nothing.
Do I have a weird module, or am I missing something?
Perhaps the extra messages are part of the protocol to indicate connection loss?

#define  Tx_Pin   6
#define  Rx_Pin   5

#include <SoftwareSerial.h>
SoftwareSerial mySerial ( Rx_Pin, Tx_Pin ); // RX, TX

#include <IRremote.h>             // IR remote control library
IRsend irsend;

// pin for the LED:
const int IR_Pin = 3;
const int FB_Pin = 8;

#define NEC   1                   // tell library to use NEC protocol
char dbg[20];
char buf[20];     // receives code from BT link
int  i;
unsigned long key;
/*
 *  Visual feedback
 */
void Blink ( int Count )
{
    for ( int j = 0; j < Count; j++ )
    {
        digitalWrite ( FB_Pin, HIGH );
        delay ( 100 );
        digitalWrite ( FB_Pin, LOW );
        delay ( 100 );
    }
}

void Blink1 ( )
{
    digitalWrite ( FB_Pin, HIGH );
    delay ( 20 );
    digitalWrite ( FB_Pin, LOW );
}
/*
 *   Get code to send via IR as ASCII HEX
 *     and return binary value in key
 */
void GetCode ( void )
{
    for ( i = 0; i < 20; i++ )
        buf[i] = 0;
    
    while ( !mySerial.available ( ) );   // wait for something

    i = 0;
    do
    {
        while ( !mySerial.available ( ) );   // wait for something
        buf[i] = mySerial.read ( );
        i++;
    } while ( buf[i-1] >= '0');

    // get rid of any trailing stuff
    if ( mySerial.available ( ) )
        mySerial.read ( );
    delay ( 2 );    
    if ( mySerial.available ( ) )
        mySerial.read ( );
    delay ( 2 );    
    if ( mySerial.available ( ) )
        mySerial.read ( );

    sscanf ( buf, "%lX", &key );
    Serial.println ( key, HEX );
}

void setup ( )
{
    Serial.begin ( 38400 );
    mySerial.begin ( 38400 );
    
//  pinMode ( IR_Pin, OUTPUT );
    pinMode ( FB_Pin, OUTPUT );
    Blink ( 8 );
    Serial.println ( "Starting" );
}

void loop ( )
{
    GetCode ( );                    // blocking
    irsend.sendNEC ( key, 32 );
    Blink1 ( );
}

you might need to clean the variable key too (after irsend)