since it's not so easy to get quark in any English-speaking countries, I think British mothers suffering from mastitis, for example, are simply advised to apply cold compresses.

literally it would be a quark poultice

but as you can't find quark in many english speaking countries it may simply be a "cooling poultice"

yep, spinatwachtel is right, cold compresses

To be fair, quark does get mentioned occasionally under natural remedies - usually with an explanation of what it is - is there any evidence that quark is better than a grated raw potato compress or raw cabbage leaves stuffed into the bra?