The Pacific Standard magazine published a critical look at this claim which is available for free on the web. It says the original study started in 2005 and may have received some attention while it was still in progress, but wasn't formally published until 2011. I believe it was published in German, but I cannot find a working link to it. It seems to have gotten a lot of attention in the international press around 2014, and the findings were somewhat exaggerated in much of this reporting. It is not that the case that the deer know where the line was and refuse to cross it, just that their learned patterns of migration show the effects of the historical border.
Here are some key quotes from the lead investigator of the original study, Pavel Sustr from 2014:
"It's going to absolutely the same place in the following years,"
Sustr says. "And because of this traditional behavior, they are still
somehow respecting the former Iron [Curtain]."
He notes that some deer are making the leap into uncharted territory,
but the winds of change blow slowly in the mountains of Central
"More animals in the last year are crossing [the border], but the
trend, or the change, is quite slow because of the traditional
behavior of the deer," Sustr says. "The young deer [during its] first
year follows its mother [and] the mother is teaching [it] the area.
So, more or less, the behavior of the mother [determines] the area
which is used by the deer in later years."
EDIT 4/17/2019: It looks like key German-language study in which this claim originated went through several publications, most recently revised in 2010. If anyone reading this understands German, picking out and translating some key quotes might be helpful.
However, the most interesting source I found in English seems to superscede the evidence from that study:
Joerns Fickel, Oleg A. Bubliy, Anja Stache, Tanja Noventa, Adam Jirsa, Marco Heurich, "Crossing the border? Structure of the red deer (Cervus elaphus) population from the Bavarian–Bohemian forest ecosystem", Mammalian Biology, Volume 77, Issue 3,
2012, Pages 211-220, ISSN 1616-5047, https://doi.org/10.1016/j.mambio.2011.11.005.
This is a genetic study which suggests that the deer are breeding across the former border.
In the years from 1994 to 1997, the genotypic
differentiation between red deer populations of the
Bavarian–Bohemian forest ecosystem was low, yet significant (FST=
0.0471,p< 0.001; Kuehn et al. 2003). In late 2009, however, that small genetic distance had even diminished and become insignificant (FST=
0.009,p= 0.383), indicating genotypic admixture between the two for-merly separated red deer populations of the
Bavarian–Bohemian forest ecosystem. This result was corroborated
by the Structure analysis, which suggested a single genotypic
cluster. The detected genotypic admixture clearly rejected the
hypothesis of a behaviourally triggered secondary enforcement of a
previously long-term interrupted (by a State border barrier) gene flow
in red deer. In contrast, our results supported the alternative
hypothesis of secondary admixture between populations from both
sides of the former border, leading to a collapse of the
earlier (even if small) genotypic differentiation.
The paragraph goes on to discuss the evidence that males in particular are moving across the former border while females are more inclined to stick with their "traditional" territory.
So overall, there may be a grain of truth to the idea that the border had a lasting effect on deer behavior, but again, popular reports have exaggerated the evidence.