Interesting to read through the comments on this topic.
Some of the responses are pretty predictable (thou shalt not ... etc.) from those unable to comprehend any deeper aspects involved.
Others show a broader tolerance and wisdom that i find heartening.

The most ironic comments are from those who reveal an open distaste for any sign of human interaction or ongoing ritual activity at these ancient ritual sites. Instead wanting them kept looking a certain way to fit their own personal view of them. This I find bizarre.
The tone of their comments usually reveal the deeper prejudices lurking behind their argument, - that other peoples personal offerings and tokens, are ‘offensive’ and the constant reference to these items
as 'rubbish' 'crap' 'tat' and ‘detritus’ in order to devalue and obscure their intended purpose. A very cheap ploy to justify their negative views on ‘those sort of people’ who ‘dump’ this stuff.
Quite unpleasant really.

With regard to the original post, after many years and much reflection, my own approach is that i would not touch or remove anything that looks like an offering or token left by another person - whatever my personal feelings towards the object. Simply, i do not consider i have the right to interfere. Especially not knowing the motivation behind such an offering.

Tut tut ... Another site where ‘those sort’ of people have tied rags to a tree, In the belief that it might help them recover from an illness.
http://www.themodernantiquarian.com/site/6458/clootie_well.html
get sharpening those axes.

I do still wonder what happened to the offending pottery cow left in the field at long Meg circle?

Alfrede