Why did they execute her? 
According to the author Belyakova (Ref. provided above) Dariya Leuchtenberg was arrested on 10 September 1937, and then interrogated by the NKVD in October. She was found guilty on all charges, and no doubt under duress, signed the documents presented to her admitting the following:
1. ... that she was the wife of Markezetti, an arrested Gestapo member,
2. ... she was connected with an intelligence-terrorist group of German political emigrants in Leningrad,
3. ... she was aware of the preparation of a terrorist act on A. Zhdanov (Communist Party leader),
4. ... she was recruited by a monarchist-terrorist organization,
5. ... her appartment was used for secret meetings,
6. ... her appartment was visited by six foreign counter-revolutionary organizations.
She was shot on November 5, 1937.
Her husband, who was shot a few months later, in January, 1938, had his case overturned posthumously in 1975, for lack of evidence. It was also found that criminal proceedings against him were falsified.
On May 11, 1989, Dariya was no longer classed as an "enemy of the people". However there is no consideration as to whether she was also found to have had 'evidence' falsified against her as well.