it's mounted on a board of which the main intention is telephony.
Deployed FPGA devices (aka no kits intended for development) usually get their configuration via bitstream from a flash device.Also, usually, those flash devices can be somehow updated by the user; but how this upgrade process is realized is probably not published by the vendor and it could require a lot of effort finding just that out.
Another issue is to get work to the FPGA device and get results out.. The existing open source fpga miners for Altera devices need JTAG access to the FPGA device which will probably be not available on your card.
But at least on Cyclone II devices you don't have to worry about encrypted bitstreams.. so there are at least some good news
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As mentioned regarding ASIC miners, would it rather be best to save the cards (and time) for their original design ?
Save the cards and your time. If the cards use a EP2C70 Cyclone-II *and* you have lots of free time: it's as good as any target/goal to start with FPGAs... if you really get the card bitcoin mining you certainly have acquired a good basis in digital design