The question is not about the intensity of the light that the LEDs can emit, nor about how long the battery will operate.
Just, do I need to put a resistance between the battery and the strip.
No, you do not need to add another resistor, this strip already has a 39Ω resistor.
With 3 LEDs and a 39Ω Resistor the LEDs will draw about 3-4 mA @ 9V. At this load a 9V alkaline will have a capacity of about 600 mAH as it discharges to 5V.
At 4 mA the forward voltage is likely to be below 9V. So it should be visible for a while. How long depends on how low the forward voltage can drop before it no longer emits light.
With 3 LEDs and 9V the resistor is going to be very efficient because the forward voltage will be very close to 9V. efficiency will improve as the battery voltage drops.
This strip was intended to draw about 60 mA @ 12V and would likely be fairly bright. At 3-4 mA not so bright but should be visible. I would guess brighter than moonlight in a small room.
You can always solder another resistor on top of the existing resistor to draw more current. Any value over 2Ω will work fine.
2Ω will give you about 50 mA.
5Ω will give you about 20 mA.
10Ω will give you about 10 mA.
The above numbers are for a fresh battery.
Do NOT short the resistor. A resistor is need to allow the LED to operate at its forward voltage. Without a resistor the LED is forced to operate at the battery voltage putting stress on the LED. It is a myth that it's okay to connect an LED(s) directly to a battery.
Below is 3 deep blue LEDs at 10 mA. Deep blue is what is under the white LED's yellow phosphor. Deep blue light is not very luminous. After the blue light is absorbed then reemitted by the phosphor it will appear to be about 10x brighter than this blue.
Keep in mind that a 9V battery is 9V for only a very short period of time.
Source: Energizer 9V Alkaline Datasheet