Any use/project for a strip (13.5cm to 2.5cm) of too tightly crocheted yarn

[CarmelaT]

I'm pretty new to crochet and at the moment I'm at a stage where I have a 13.5cm to 2.5cm strip of cloth for a pillow case, however I've crocheted it too tightly and now it will no longer be able to fit the pillow I've been modelling and it's too rough to actually use on something like a pillow case. Any ideas on the type of project I can try to take on going forward? Given how rough it has become and its length. 

[Granny Square]

Welcome to the 'ville!

Are you talking about a doily-thread strip of lace that size?  (for us in the US that's 5-ish" x 1").  And by rough, do you mean the lace is so tight it's stiff?

Deep breath - hold - exhale slowly.  OK, now rip it out and try again with a bigger hook, and focus on loosening up your tension.  This requires  some concentration and effort, but you can do this - I had the same issue when I was new at crochet and had to learn to loosen up too.  If you are using a tapered hook, make sure you don't form the stitches right at the tip of the hook, pull each stitch back to the thick shaft part which is the part that 'sizes' the stitches.

As to ripping, this is part of the process unfortunately.  When you rip and re-do (like fixing a mistake x rows down), the re-doing seems to go faster, I'm sure that's my imagination but it makes me feel a little better about it.  There's no point in keeping a little oddment of lace and wondering what to do with it when you can re-purpose the yarn for something that you will be happy about finishing and putting to good use.

Back to hook sizes and yarn or thread; first assuming thread because of pillowcase edge, the most common thread size used in modern patterns is #10, and I'm a bit of a doily-head and usually use a US#7 steel (1.65mm) hook, but I've used all the way up to a US C 'yarn' hook (2.75mm).  And if you like working with thread, maybe try coasters or 'mug rugs' to practice getting your tension where you like it.