I would think that the cemetary has restrictons on who has the right to put a headstone on a grave, and it would be limited to the owner. Check your written sales documents with the cemetary for the plot.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.
There are specific laws regarding who can place a headstone on a grave. Health and Safety Code Section 7100 states that the next of kin has the authority to deal with headstones. First in line are you and your siblings, then your grandmother. The non-family member has not authority to place a headstone.