[12] Before the 10th KSČM congress in Nymburk on 21 April 2018, Konečná unsuccessfully challenged Vojtěch Filip as leader of the party.

[15] On 23 October 2021, Konečná was elected the first chairwoman of the Communist Party of Bohemia and Moravia, replacing the long-time chairman Vojtěch Filip.

Konečná is mentioned in the Transparency International report revealing the details of the Azerbaijan Laundromat money-laundering scandal.

[18] In 2013, when Konečná was a member of the Czech Republic-Azerbaijan friendship group, she was among the supporters of the resolution "on the 21st anniversary of the Azerbaijan massacre".

The resolution was widely criticised on the grounds that it was "biased and did not contribute to the fair relations of the Czech Republic with the region of the South Caucasus".

[19] As a member of PACE, Konečná voted against the motion of resolution on political prisoners in Azerbaijan, which was not adopted.