Checking that your client can read & write assists both you and them. Attempting to use questionnaires, journals or bibliotherapy with someone hiding their illiteracy could end your intervention before it has begun.
Literacy isn't essential in therapy: psychological therapies aren't called "talking cures" for nothing and physical therapies usually require little in the way of reading or writing. Clients who cannot write can keep pictorial records or use voice recorders (now built into many mobile phones) to keep notes of thoughts or actions. Much of the literature therapists would wish to hand out to clients could, with a little effort, be offered as graphics or video & audio recordings.
The difficulty for most therapists will be in identifying clients whose illiteracy may be one of their most closely guarded and shameful secrets. Ticking the boxes on your questionnaire need not mean that the questions have been read. Phrases like "your writing is too small" or "I've left my glasses at home" may mean exactly what they say, or may be well-practiced cover-up routines. Allocating an illiterate person to bibliotherapy can be a waste of their time and yours.
Many people who cannot read nevertheless have a "social sight vocabulary": they can recognise words and phrases commonly seen on signs (eg: "school", "exit", "this way") by the shape of the word. They can also write familiar personal phrases (eg: name, address, signature) which are usually all that is required on most official forms. This may be sufficient: they may not wish to expand their range and your therapeutic intervention may be deliverable at this level.
If your therapeutic intervention does require the client to be able to read or write, you can build a quick check into your first session. A brief questionnaire such as a symptom checklist or consent form can be constructed to require entry of data beyond the familiar vocabulary of name, address or signature. The text of the form should be set in a large clear font.
If you are going to check your client's literacy, "false positives" can be reduced by asking in your appointment letter for clients to bring reading glasses if they need them. Similarly, if you are told "I've left my glasses at home", re-presenting the form at the next session might be better than assuming illiteracy there & then. Taking the form home to complete should not be an option, for obvious reasons.
Using this approach requires a degree of sensitivity and thought. Exposing an inability the client has sought to conceal will probably be extremely embarrassing for them and you will need to work hard to maintain them in therapy. Think again: is there really no alternative to writing or reading in the therapeutic approach you wish to use?
For some clients, their illiteracy may be a significant part of their reason for engaging in therapy. In the UK, those wishing to improve their reading or writing can be directed to learn direct on 0800 101 901.