Here's an LPSC report showing similar thermal infrared spectra for oxidized olivine as for unweathered olivine:

THERMAL EMISSION SPECTRA OF RED, OXIDIZED OLIVINE: IMPLICATIONS FOR OLIVINE ON MARS.
M. D. Kraft, T. G. Sharp, A. Trueba, and T. R. Diedrich, Department of Geosciences, Arizona State University, Tempe, AZ 85287-1404; mdkraft@asu.edu.
Lunar and Planetary Science XXXIII (2002) 1964.pdf
http://www.lpi.usra.edu/meetings/lpsc2002/pdf/1964.pdf

An image on this page shows the appearance of the green unweathered olivine as opposed to the red oxidized olivine:

posted November 7, 2003
Pretty Green Mineral -- Pretty Dry Mars?
Written by Linda M.V. Martel
Hawai'i Institute of Geophysics and Planetology
--- The discovery of olivine-bearing rocks on Mars underscores the need to understand weathering rates of silicates in the Martian environment.
http://www.psrd.hawaii.edu/Nov03/olivine.html

Then depending on the amount of the olivine in the soil, accurate color imaging might help to distinguish between the two possibilities.

It is notable that in the LPSC report of Kraft et.al. the band depths of the oxidized olivine are shallower than that of the unweathered olivine. Then this might be used as a measure of the degree of oxidation.

The Science paper of Hoefen et.al. discussing olivine in Nili Fossae does not mention the spectra of oxidized olivine which leads me to believe they did not make the comparison:

Discovery of Olivine in the Nili Fossae Region of Mars
Todd M. Hoefen,1* Roger N. Clark,1 Joshua L. Bandfield,2
Michael D. Smith,3 John C. Pearl,3 Philip R. Christensen2
SCIENCE, VOL 302, 24 OCTOBER 2003, p. 627-630.
http://www.higp.hawaii.edu/~hamilton/rem_sens/papers/Hoefen_Science.pdf

It is also interesting that in an LPSC report of Hoefen and Clark (no relation) that compares the spectra of Nili Fossae and Terra Meridinai and spectra of olivine samples:

Compositional Variability of Martian Olivines Using Mars Global Surveyor Thermal Emission Spectra.
T.M. Hoefen1 and R.N. Clark1, 1U.S.Geological Survey (thoefen@speclab.cr.usgs.gov, rclark@speclab.cr.usgs.gov).
Lunar and Planetary Science XXXII (2001) 2049.pdf
http://www.lpi.usra.edu/meetings/lpsc2001/pdf/2049.pdf

that the bands in the spectra of Terra Meridiani are also shallower than those of Nili Fossae and of the unweathered olivine samples.
This would be consistent with the idea of liquid water weathering at Meridiani if there is a connection between band depth and degree of oxidation.

However, it should be said that Hoefen et.al. mention that the size of the particles can also effect the band depths. So it might be difficult to distinguish this effect from the effect of oxidation.

Another relevant factor might be the FeO content. Kraft et.al. mention there was a shift near 420 cm^-1 to higher wave numbers for the oxidized olivine. And both the Science paper and LPSC report of Hoefen et.al. mention that at wave numbers in the range from 600 to 300 cm^-1 there is a shift towards higher wave numbers with increasing FeO. Then high FeO content might be the case with the oxidized olivine studied by Kraft et.al.
However, Kraft et.al. also mention there is a shift towards *lower* wave numbers with the oxidized olivine near 945 cm^-1. Then this might be used as a confirming factor in the spectral analysis of Mars in regards to the oxidation of the olivine. However, the Hoefen et.al. reports do not consider this higher spectral range to avoid confounding their results with the spectral signatures of atmospheric dust and water vapor. In particular there is a dust band at 1100 cm^-1. This might be far enough away from 945 cm^-1 so that they can make a comparison to the oxidized olivine and the olivine seen on Mars in this spectral range.

I don't know if there is also a similarity in the Mossbauer spectra of oxidized olivine as compared to that of unoxidized olivine. It was the Mossbauer instrument on Spirit that detected olivine at the Gusev site. However, an expert on Mossbauer spectra has expressed doubts about the ability of the Mossbauer instrument on the MER rovers to determine if minerals are in hydrated form or not:

Concern voiced on rover rock data
By Paul Rincon
BBC News Online science staff
The Moessbauer spectrometer is a key instrument on Spirit
The device used by Nasa rovers to study minerals on Mars could return confusing results, complicating the search for signs of water, an expert has said.
http://news.bbc.co.uk/2/hi/science/nature/3411227.stm

Bob Clark