It is not a matter of HKD3580 or HKD4000 or HKD5000. It seems to me that she has planned to take a chance to chat with you for demanding higher salary.
If she has planned looking for higher salary, you cannot stop her even you give her HKD4000 today, but later because some friends tell her that they can earn even higher from other employers in HK or in other countries, then she will ask again, or thinking of going somewhere again.
If it was me, I would let her go. And there is still some months before the contract finishes, I would start looking around for other domestic helpers, instead of being "controlled" by what she can hear from her friends.
If you increase her salary because she asks you so, definitely you have opened the door to let her ask you for more things like further increase in salary, or better benefits, or more holidays or more flexible holidays. This is because you have proved to her and strengthened her thinking that she is indispensable. And I can predict that her attitude will first be very thankful to you, then after a short period of time, say 2 or 3 months, will change to very bad working attitude or she will put her position very high in your house.
You know it is different from what if you take the intiative to give her bonus instead of being asked or "threatened" to increase salary.