It's easy to over-ink your block when you're first learning linocut. It's actually just as easy to do even when you're been printing for a while when you get to a point where you're inking blocks with lots of fine details.
When I'm printing blocks with lots of these very fine marks, I keep a tissue to hand to blot my block just as you would with painting. After I've pulled each print, before I roll the next lot of ink on, I use a tissue to press all over these 'trouble spots' where the fine details are. Sometimes I even find it necessary to use my nail to gently push the tissue between these lines if they are very fine.
^Blocks like this one are a good example. Even though I think I've been careful rolling the ink out, the lines I've carved into the bottom of the bottle are so thin it's very easy to saturate them and infill them with ink. You can see on the left how I do this between each print.
An old rag/cloth would work just as well as a tissue and maybe better in a lot of cases as some tissues can shed fibres that can stick to the ink or block.
My blackbird print below is another example of a trouble spot where I have to do this- the beak gets very easily filled with ink as I've carved the line fairly shallow. It's a time consuming process but worth the trouble of course. Once you've done a couple of test prints you'll likely know where your trouble spots are.