What you are looking for is a receiver with an RSSI function (Received Signal Strength indication); this is usually an analog output proportional to the log of the signal strength.
The datasheet does not give particularly good specs, as is common with the Sparkfun datasheets I have looked at. If you could identify the real manufacturer, they might have better data.
In this case, that takes us to a page on www.rf.net.tw which has exactly the same data sheet. However it does have an "Ask Question" form where you could ask if this module has an RSSI function. (Be prepared for the question to be ignored or misunderstood, but it may be worth a try).
The datasheet DOES say "Modulate Mode : ASK" which means "Amplitude Shift Keying" which means the linear output MAY vary in voltage to some extent with signal strength, but probably not enough to be useful, because AGC (automatic gain control) will keep the output signal almost constant.
One of the comments on the Sparkfun page talks about using the linear output for RSSI and links to this page about it. Doesn't look very reliable to me.
This page describes digging into a similar module (different manufacturer) and finding an undocumented RSSI signal, if you are brave enough.
All of which probably leaves you looking for another receiver : this time, search for "315 MHz receiver with RSSI" and you may find something more useful.
Reading the question and the comments, there may be a conceptual misunderstanding : the attenuator WILL attenuate any noise presented on its input (even from just a 50 ohm source impedance), to the same extent it attenuates the signal.
However it also generates noise of its own, which may be represented as the noise from a perfect resistor equal to its own output impedance, and this is added at the output to the (attenuated) input signal and noise. So if input and output Z are both 50 ohms, the net result is attenuated signal + marginally increased noise (i.e. NF = attenuation).
But if its output impedance is lower, the added noise is also lower, thus improving the noise voltage as Andy states.
So represent the attenuator as a perfect attenuator (attenuating noise) in series with a Johnson noise voltage source equal to the output impedance. The rest is just applying the formulae.
EDIT: re: updated question.
(1) There is nothing special about 290K except that it's a realistic temperature for the operation of a passive circuit. The reason they chose it is that the article quotes a noise floor ( -174dBm/Hz) which is correct for a specific temperature : yes, 290k.
(2) While any resistance in the attenuator will contribute noise, I realise that it is not a satisfactory explanation as to why you get the same noise out of an attenuator, because (as Andy says) you could make a capacitive attenuator which is not a Johnson noise generator. So we have to look a little deeper, and remember these noise sources are the statistics of the individual electrons that make up the current.
So, let's say we build a (50 ohm in, 50 ohm out) attenuator, and attempt to cheat Johnson by using a capacitive divider. That implies a node within the attenuator which conducts some of the input current to ground. At this node, we have two current paths; a fraction of the current flows to output, the rest to ground. What determines which path an individual electron will take? Essentially, chance. Collectively? Statistics. So this is a noise source.
Or let's just add series capacitance to provide enough attenuation : we thereby avoid dividing the current flow and eliminate the noise source, right? At the cost of reducing the signal current; our statistics now operate with a smaller sample size and consequently greater variance : more noise.
These results are the best you can do, there is no way round them.
Best Answer
A log scale here feels much more intuitive to the average user than a linear scale, as long as you don't tire them (consumers) with dBm details.
If your range is -100 to -40 dBm, I'd map -100 to a small percentage, say 5% and -40 to 100%. That is assuming you can still receive a signal at -100dBm and you have a separate indicator that your receiver is not locked => 0%
So when locked: $$percentage = \dfrac{19}{12}×register + 163\dfrac{1}{3}$$
When unclocked: $$percentage = 0$$