As seen in the photos below from https://terra.nasa.gov/about Terra is reddish, so the answer to
Why is Terra reddish?
is exactly what you have suspected; because it is wrapped in a thermal protection film that is reddish in color.
However, the answer to a more interesting question:
Why am I surprised that Terra appears reddish?
would have several components.
Many spacecraft are overwrapped in a neutral color film that appears silvery or various shades of gray. The engineering choice is related to thermal management of the whole spacecraft, where incoming visible and near-infrared light from the Sun carries about 1360 Watts in every square meter, visible and thermal infrared heating from the Earth, and the rest of space which offers almost no heating but readily accepts the spacecraft's thermal radiation which cools it. For some reason Terra is wrapped in this particular film, which is reddish in color.
Terra carries ASTER the Advanced Spaceborne Thermal Emission and Reflection Radiometer which images a wide range of wavelengths including thermal infrared out to 11.65 microns. It uses a 1.2 Watt Stirling cryocooler that reaches down below 80 K (1, 2, 3) and keeping the cryogenically cooled infrared sensor and optics sufficiently cold may have required this particular thermal overwrap material.
It is sometimes difficult to judge the color of star-like objects. Color perception is a broad science, but there are at least two things at play here. For dimmer star-like objects it becomes difficult to judge the color because of the way our vision system works, especially in the central area of vision (e.g. rods and cones). It may be that you have looked at other satellites that had colors that were not neutral and simply didn't notice the color, or did but dismissed it (e.g. expectation bias or choose another from this list of cognitive biases). At the same time, when viewing a bright star-like object using good light-collecting binoculars, some spacecraft with a discernible color may have been too dazzlingly bright in your dark-adapted eyes, so you may have missed some non-neutral colors before.
Images from https://terra.nasa.gov/about In reflected sunlight the spacecraft will probably appear roughly this color at night under ideal observing conditions, but see above for some of the ways that one can be thrown off.