Some more info.
Image of the controller card:
The wires are soldered onto the SD Card holder:
Oscilloscope screen of the CS line, different time scale:
The whole write cycle is about 120 ms and is repeated every 5 seconds. CS line is dropped high/low several times during one write. A better way not to interfere with the write operation would be to look for low to high transition on CS line and then wait for say 250 ms before reading the card.
Oscilloscope screen of the SCK line, different time scale:
Clock frequency is 4 MHz and, one byte takes 2 us and the delay between bytes is 4 us.
Ideas are welcome!