You can check this yourself, but need a second person to help with flushing.
First check if you have any water saving device in your toilet cistern (such as a pouch or brick) and temporarily remove, to increase water volume. (not essential but helpful)
Lift your drain inspection cover outside, get the toilet flushed while you watch outside to see if what's coming through is as expected.
If you have a rat prevention trap at the drain outlet, you may find the cloth caught there. If no sign of it and water flushes through freely you're almost certainly fine, and it's flushed into the main drainage system which should cope.
Assuming the extra water running into the bowl, isn't causing the the level in the toilet bowl to rise, this is likely to be a co-incidental issue that you haven't previously noticed.
Generally the most common reason for water running slightly into the toilet, is the flush valve (flapper) at the bottom of the cistern has deteriorated. If it doesn't seat properly, water will continuously leak into the toilet bowl.
If it's always done it, it's likely the float height needs adjusting, (you can do yourself) or less likely, the fitting has been bodged and you need to shorten or lengthen the flush tube.