フォームにTButtonを２つ貼り付けてください。

#include <vcl.h>
#include <Registry.hpp>     // ← 要追加

#pragma hdrstop

#include "Unit1.h"
//---------------------------------------------------------------------------
#pragma package(smart_init)
#pragma resource "*.dfm"
TForm1 *Form1;

// 下記1行を追加、TESTの部分は任意の文字列
#define Reg_Key "SOFTWARE\\Microsoft\\Windows\\CurrentVersion\\Uninstall\\TEST"

//---------------------------------------------------------------------------
//  機能:「プログラムの追加と削除」への登録
//---------------------------------------------------------------------------
void __fastcall TForm1::Button1Click(TObject *Sender)
{
        TRegistry *Reg = new TRegistry;

    Reg->RootKey   = HKEY_LOCAL_MACHINE;
    Reg->LazyWrite = false;
    if( Reg->OpenKey(Reg_Key,true) ){
        Reg->WriteString( "DisplayName", "てすとぷろぐらむ" );
        Reg->WriteString( "UninstallString", Application->ExeName );
        Reg->CloseKey();
    }
    delete Reg;
}


//---------------------------------------------------------------------------
//  機能:「プログラムの追加と削除」からの削除
//---------------------------------------------------------------------------
void __fastcall TForm1::Button2Click(TObject *Sender)
{
        TRegistry *Reg = new TRegistry;

    Reg->RootKey   = HKEY_LOCAL_MACHINE;
    Reg->LazyWrite = false;
    Reg->DeleteKey( Reg_Key );
    delete Reg;
}